There are $n$ identical balls and we need to put them inside $n$ baskets. What is the probability that all the balls are in $1$ basket if it is known that there are at least $k$ empty baskets ($0 \leq k \leq n-1$).
Because we know something before it is something to do with $P(B \mid A)$, but I am not sure how I should do this.
$$ \textsf P(n-1\text{ empty}\mid k\text{ empty}) = \frac{\textsf P(n-1\text{ empty}\cap k\text{ empty})}{\textsf P(k\text{ empty})}=\frac{\textsf P(n-1\text{ empty})}{\textsf P(k\text{ empty})}\;. $$
The numerator is easy; the denominator can be obtained using inclusion-exclusion.