MathNet 2023 — batch of 35 questions Question 22

There are $800$ marbles in a bag. Each marble is colored with one of $100$ colors, and there are eight marbles of each color. Anna draws one marble at a time from the bag, without replacement, until she gets eight marbles of the same color, and then she immediately stops.

Suppose Anna has not stopped after drawing $699$ marbles. Compute the probability that she stops immediately after drawing the $700$th marble.