Suppose there is a set $S_1= \{c_1,c_2,...,c_n \}$, we create subset $S_{i+1} \subseteq S_i$ as follow:
$\forall c_j \in S_i;1 \leq j \leq n $ we toss a coin, if it is head we pick $c_j$ to be inserted in $S_{i+1}$ else it will not.
We repeat this until we reach to $S_h \ne \phi $ and $S_{h+1} = \phi$ (infact this data structure is a skip list). The expected value of $h$ which is number of $S_i$s (its height) equals to $\log n$, $$PR(height = h) = n/2^h $$ if $$n/2^h = 1 \rightarrow 2^h = n \rightarrow h = \log n$$
Now it has been claimed that
There is a positive constant $c$ such that for all sufficiently large real numbers $s$, we have $$PR(h\geq s \log n) \leq 1/n^{cs}$$
I really have no idea how to prove it (may be Chernoff bound is needed!)