A jar contains a marble, it may is black or white with the same probability.

We put a white marble in the jar and then we draw a marble. Suppose that the marble we draw is white. What is the probability the first draw to be black?

Facts:

W: the first marble is white, B: the first marble is black.

DW: we draw a white marble, DB: we draw a black marble.

I think the answer is 1/2 but how can i proove it ? Can anybody help me ?