Keeping It In the Family

Sometimes, while learning Talmud and the commentaries, one can uncover new facts about the events recorded in Tanach.
Tosfos in Yevamos (21a) states that Dovid HaMelech married the former wife of Shaul HaMelech, Ritzpah Bas Aya. There is no mention of this fact in the entire Tanach or the entire Talmud Bavli. Dovid HaMelech married Michal, Shaul’s daughter. So when he married Ritzpah Bas Aya, he was marrying his father-in-law’s widow. This proves that one is allowed to marry his father-in-law’s former wife that is not his mother-in-law. The Talmud Yerushalmi states, though, that even though this is permitted on a Torah level, it is forbidden rabbinically because of maaris ayin. It would appear to an onlooker that one is marrying his mother-in-law, which is a Torah prohibition. It is possible that this prohibition did not apply to Ritzpah Bas Aya. She was an agunah because, as the widow of Shaul HaMelech, she could not marry anyone else besides another king.
However, the Talmud Bavli does not mention this prohibition. This leads many Rishonim to conclude that, as a practical matter, we do not follow the Yerushalmi on this matter.