(Mishnah): If there are rumors in the city that a woman became Mekudeshes, she is [established to be] Mekudeshes. [If rumors say that she was] divorced, she is [Muchzekes] divorced. This is only if there is no excuse (a way to discredit the rumors).

What is an excuse? Ploni divorced his wife on condition, or he threw her Kidushin money to her, and it is a Safek if it landed closer to her or to him. This is an excuse (why there are rumors. In truth, perhaps the divorce or Kidushin was found to be invalid!)

(R. Yosa citing R. Yochanan): [Our Mishnah is only when] there were lamps burning and people were talking.

Question (R. Ze'ira, to R. Yosa - Mishnah): If there are rumors in the city that a woman became Mekudeshes, she is Mekudeshes. [If rumors say that she was] divorced, she is divorced;

[When they say that she was divorced,] can you say that there were lamps burning?! No, [just] people were talking [and this suffices. Also for Kidushin], people were talking [and this suffices].

(R. Yosa citing R. Yochanan): If they checked the name (the rumors, and) it was found to be women and minors, the name (rumors) is Batel.

(Rav): They permitted [to be Mevatel rumors] only when one 'witness' heard from one witness (i.e. only one person allegedly saw, but not if there are two, e.g. Reuven heard from Shimon and Levi heard from Yehudah - RIVASH 504).