Say I generate $N$ random integers called $X_i$, where $1 \leq i \leq N$.
The first random integer is chosen uniformly from the set of integers $[1, K]$. For $2 \leq i \leq N$, $X_i$ is chosen uniformly from $[X_{i-1}, K]$. In other words, each random integer is lower bounded by the previous random integer.
What is the probability that $X_N = K$?