The probability of event A happening given that event B already
happened is the probability of A and B happening divided by the
probability that B happened. This can be pressed as Pr(A|B)=Pr(A and B)/Pr(B).

In this case A is drawing a black marble and B is having already drawn a
black marble.

Pr(A and B) = (1/2) * [(3/4)^{2} + (1/4)^{2}] = 5/16.