This belongs to the category of conditional probability, and every touch of the ball is no longer an equal probability event. You can refer to the probability of drawing lots. Several people draw lots together, but they don't know each other's lottery. Everyone draws lots with equal probability. But once you know the result of someone's smoking, the probability of smoking again is not equal. Because the total number of samples has changed.
This problem is similar to the lottery principle of calculating the probability that the last two times are also white balls after knowing the first two times.