How to understand a mathematical probability problem is the correct explanation?

Assuming that the probability of A winning is 0.3, the probability of the remaining 9 cards winning is 2/9.

The probability of A not winning is 0.7, so the probability of winning the remaining 9 cards is 3/9.

The winning probability of B is 0.3X 2/9+0.7X3/9 = 0.3, so the winning probability of B is the first winning probability of 0.3 =.

What you think has not been worked out yet. You have to multiply it by the first probability to work out the second time.