1) THE PROHIBITION OF A "SAFEK SOTAH"
The Gemara teaches that the verse of "v'Nitma'ah" (Bamidbar 5:29) teaches that a Safek Sotah is prohibited to her husband after Kinuy and Setirah.
(a) Why is it necessary for a verse to teach that a Safek Sotah is prohibited to her husband? Since she is suspected of having relations with another man, she should be prohibited because of the principle of Safek Isur. (TOSFOS DH Mah)
(b) Even if a Safek Isur is normally judged leniently, there still is no necessity for a verse to prohibit the Safek Sotah. Even without the verse there is reason to be stringent and prohibit the woman because, as the Gemara says in Nidah (3a), when the woman secludes herself with another man after Kinuy there is "Raglayim l'Davar" that she sinned. (TOSFOS DH Eino)
(a) TOSFOS explains that the reason why a Safek Isur is normally treated stringently is that it is necessary to suspect the worst. When a person takes the risk of doing an act which may involve a transgression of a Torah law, but it turns out that no Isur was involved, he has not transgressed a Mitzvah of the Torah. (Rather, he merely needs atonement for not being cautious of the Safek Isur. See Nazir 23b.) In contrast, the prohibition of a Safek Sotah to her husband is an independent Mitzvah (a Mitzvas Aseh of "v'Nitma'ah"; some even say that Malkus is administered for transgressing this Mitzvas Aseh -- see Tosfos to Yevamos 11b, DH Mai, and Insights to Sotah 7:1:a).
Similarly, when an object which is Safek Tamei is found in Reshus ha'Yachid, the rule is that it is considered definitely Tamei, and if it is an item of Terumah it must be burned. (However, in contrast to the case of Sotah, in the case of Tum'ah if the Safek is clarified and it is determine that there was no Tum'ah, retroactively anything which touched the object is Tahor.)
Alternatively, without the verse of "v'Nitma'ah" a Safek Sotah would be permitted to her husband because she has a Chezkas Heter that she is permitted to him. The verse of "v'Nitma'ah" teaches that the Chezkas Heter does not apply. (See Tosfos to 28b, DH mi'Kan.)
(b) TOSFOS explains that without the evidence of "Raglayim l'Davar" there is not even a doubt that the woman committed adultery, because no Jewish woman is suspected of committing such terrible transgressions (she has a Chezkas Kashrus). The "Raglayim l'Davar" transforms the situation into a Safek -- but it remains a Safek until the verse of "v'Nitma'ah" teaches that she is Asurah mi'Vadai, prohibited for certain, with no doubt.
The RASHBA in Kesuvos (9a) explains that the "Raglayim l'Davar" offsets the woman's claim of certainty (her "Ta'anas Bari") that she knows for certain that she is Tehorah, and it makes her case into a case of Safek.
Rebbi Shimon in Nidah (3a), however, rules that when there is no "Raglayim l'Davar," a Safek Tum'ah in Reshus ha'Yachid is indeed Tamei only mi'Safek. In the case of Sotah, the "Raglayim l'Davar" together with the verse of "v'Nitma'ah" makes her prohibition into a Vadai.
2) "SAFEK TUM'AH": THE DIFFERENCES BETWEEN "RESHUS HA'RABIM" AND "RESHUS HA'YACHID," AND BETWEEN "DAVAR SHE'EIN BO DA'AS LISHA'EL" AND "DAVAR SHE'YESH BO DA'AS LISHA'EL"
OPINIONS: The Gemara teaches that an item that is a Safek Tum'ah in Reshus ha'Yachid is deemed Tamei, but only when that item is a "Davar she'Yesh Bo Da'as Lisha'el." An item that is a Safek Tum'ah in Reshus ha'Rabim, or a "Davar she'Ein Bo Da'as Lisha'el" even in Reshus ha'Yachid, is deemed Tahor.
The Rishonim discuss whether the Safek Tum'ah in Reshus ha'Rabim is Tahor because of its Chezkas Taharah (Tosfos to 28b, DH mi'Kan) or because of a special Halachah l'Moshe mi'Sinai which states that even when there is no Chazakah a Safek Tum'ah in Reshus ha'Rabim is Tahor (Tosfos to Chulin 9b, DH Hasam).
The Gemara derives these Halachos of a Safek Tum'ah by comparing Tum'ah to the Isur of a Sotah. The Gemara in Chulin (9b) refers to this as "Hilchasa Gemira Lah mi'Sotah" -- a Halachah l'Moshe mi'Sinai derived from the Halachos of Sotah. However, even if these differences (between Reshus ha'Rabim and Reshus ha'Yachid, and between "Davar she'Yesh Bo Da'as Lisha'el" and "Davar she'Ein Bo Da'as Lisha'el") are a Halachah l'Moshe mi'Sinai, there should be some logic behind them. Is there any way to logically justify the difference between Reshus ha'Rabim and Reshus ha'Yachid, and the difference between "Davar she'Yesh Bo Da'as Lisha'el" and "Davar she'Ein Bo Da'as Lisha'el," with regard to the status of an item that is Safek Tum'ah?
(a) TOSFOS (28b, end of DH mi'Kan) and the RA'AVAD (Hilchos Avos ha'Tum'ah 16:1) cite a Tosefta which states that the reason why a Safek Tum'ah in Reshus ha'Rabim is Tahor is that "Iy Efshar Lish'ol l'Rabim" -- it is impossible to ask the populace if the item or person is Tamei or Tahor.
The Tosefta implies that the logic for being Metaher a Safek Tum'ah in Reshus ha'Rabim, and the logic for being Metaher a Safek Tum'ah which is "Ein Bo Da'as Lisha'el," are based on the same point: when it is impossible to clarify through interrogation whether the item is Tamei -- either because only inanimate items are involved or because it is not known who was present at the time the Safek arose -- the Torah does not make the item Tamei. (Since it is normally not known who was present in Reshus ha'Rabim at any given moment, and it normally is known who was present in Reshus ha'Yachid, the Torah does not differentiate between each specific case, whether or not it is known who was there.)
Why, though, should the Tum'ah depend on whether there is someone available to ask about it? Apparently, the Torah makes the object Tamei since its Tum'ah is able to be clarified. When the doubt can be clarified, the Torah does not want us to rely on the Chezkas Taharah to make it Tahor. This is consistent with the opinion of Tosfos here who writes that a Safek Tum'ah in Reshus ha'Rabim is Tahor only because of the Chezkas Taharah (and when there is no Chezkas Taharah, it is Tamei).
A similar opinion is that of TOSFOS (DH b'Reshus ha'Rabim) and the TOSFOS HA'ROSH (end of Nidah 2a) who write that a Safek Tum'ah in Reshus ha'Rabim is treated leniently because the Safek "can be revealed to all" -- that is, the true status of the object tends to be known by all. The logic behind this might be that in Reshus ha'Rabim it is not necessary to investigate whether the object is Tamei or not, because had it been Tamei someone certainly would have spoken up about it. Hence, there is a strong reason to assume that it is Tahor, and that is why the Torah is lenient and relies on the Chazakah and assumes that the object's status did not change and it remained Tahor in a case of a Safek Tum'ah in Reshus ha'Rabim.
Why, though, is the Torah lenient in the case of a Safek Tum'ah which is a "Davar she'Ein Bo Da'as Lisha'el"? The ROSH there writes that when the item can be asked about the Tum'ah, it is possible to clarify the Safek, as the Tosefta says, and the Torah requires us to clarify the Safek whenever possible, even in Reshus ha'Yachid. (Tosfos here (DH b'Reshus ha'Rabim) seems to imply that even if there is a logical reason to differentiate between a Reshus ha'Rabim and a Reshus ha'Yachid, there is no logical reason to differentiate between "Yesh Bo Da'as Lisha'el" and "Ein Bo Da'as Lisha'el." However, Tosfos (in DH mi'Kan) seems to say that there is not even any logical reason to differentiate between Reshus ha'Rabim and Reshus ha'Yachid. Rather, it is all a Halachah l'Moshe mi'Sinai with no apparent reason.)
(b) The VILNA GA'ON (Chidushim, Maseches Taharos 5:1 and 6:1, printed in the Vilna Shas) writes that the Torah is lenient in the case of a Safek Tum'ah in Reshus ha'Rabim because it is more common for doubts to arise with Tum'ah in Reshus ha'Rabim since so many people traverse there. Similarly, when the object is a "Davar she'Ein Bo Da'as Lisha'el," it is more common for doubts to arise because there is no person involved who is trying to avoid the Safek. Therefore, the Torah is lenient. (RAV M. HELLER)
The Vilna Ga'on seems to understand that the Torah wants to make it easier for those who work with Taharos, and, therefore, it rules that one may be lenient in cases where doubts arise often. This is similar to the Halachah taught in the end of Chagigah, that during the festival, when more Amei ha'Aretz come to Yerushalayim, what they touch is treated as Tahor and the normal Chumros are suspended.
The logic of the Vilna Ga'on is easier to understand according to the opinion of the RAMBAM (Hilchos Avos ha'Tum'ah 16:1), who writes that the reason why "the Chachamim were Metaher Tum'ah in Reshus ha'Rabim" is "because all of the Sefeikos are only Isurei d'Rabanan," and he adds that one should see what he writes elsewhere (in Hilchos Isurei Bi'ah 18:17), where he writes that every Safek d'Oraisa is judged leniently, l'Kula, mid'Oraisa, and it is only mid'Rabanan that we are Machmir in cases of Safek d'Oraisa. Here, the Rabanan were lenient out of necessity, as the Vilna Ga'on explains.