I don't think you can solve this without more information. For example, if all you have is white balls to fill the bag, then the probability is obviously 1. On the other hand, if white is just one of an equally likely million colors, the probability will be close to 0.

This is only right if you assume that the the a priori probabilities of cases A, B and C are all 1/3. That fact should have been given in the question.