This is a simple probability question. You have n slots out of which you are never supposed to select last k slots.
i.e. You have n slots and you should always select out of first n-k slots for an insertion. And this will happen r times.
Probability for 1 insertion = $\dfrac{n-k}{n}$
Probability for r insertions = $\dfrac{n-k}{n} × \dfrac{n-k}{n} × \dfrac{n-k}{n}$ ... r times
= $(\frac{n-k}{n})^r$
= $(1 - \dfrac{k}{n})^r$