Use the fact that the probability of Y occurring given X has occurred (a general X) is simply the marginal probability distribution of Y. This differs from the normal joint conditionals, in that there is no explicit value of X being given here. But that's ok, don't need one. You just have to do some math simplification. Have you tried actually starting the right side of the equation using the formula you already know? You know that E(X|Y) is just an expression. So plug that expression in and see what you get.