Kiddushin 62 - Mistaken But Valid Betrothals And Those That Can't Happen Yet

If one betrothed a woman and subsequently said, "I thought that she was the daughter of a Kohen, but in fact she is the daughter of a Levi", or vice versa; "I thought that she was poor, but in fact she is rich," or vice versa - the woman is betrothed, because she did not mislead him.

If one performs an act of betrothal and tells a woman, "Become betrothed to me after I convert to Judaism" or "after your husband dies" or "after your sister (my current wife) dies" - she is not betrothed even after the specified event takes place.