Clarification about this post: The order statistics of uniform distribution $U_{n,k_n}→p$ a.s., when $K_n/n→p$

Question

Could anyone elaborate a bit on the question of this post or provide a reference for it: The order statistics of uniform distribution $U_{n,k_n}\rightarrow p$ a.s., when $\frac{K_n}{n} \rightarrow p$

Does it mean we randomly select $k_n$ according to a distribution and $U_{n,k_n}$ converged to the mean of that distribution? @Knotnet