Let's consider the following set of books from which a winner can get 2 books:
Books = {Physics1, Physics2, Physics3, Math1, Math2, History, philosophy}

Let's write:
A is the event associated to "win a Physics book", and B is the event associated to "win a Math book"

The probability to win, at first, a Physics book, is: P(A) = 3/7

The probability to win a Physics book and then a Math book is: P(A ∩ B ) = 3/7 x 2/6 = 1/7

What is the probability to win a Math book given that it have been, at first, won a Physics book ?

P(B/A) = p(B ∩ A)/p(A) = (1/7) / (3/7) = 1/3 = 33%

The conditional probability of an event B linked to an event A is the probability that event B occurs given that the event A has already occurred.

The probability of B given A is :