The probability of selecting a marble that is not black is 9/12=3/4.
The probability of selecting a white marble is 5/12 if all the marbles are available for selection.
If the black marbles are now withdrawn, leaving 9 marbles, then the probability of selecting a white marble becomes 5/9.
If the two probabilities are combined we have 3/4*5/9=5/12, the same as before.