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.