The alphabet is supposed to have $n$ characters (usually $n=26$, though in my case $n=256$ or $256^2$ or $256^4$). 

**Example**: 

Here $n=2$ and the alphabet consists of two letters A and B. The prespecified sub-sequence is ABB (so $K=3$). The sequence contains $M=4$ letters. The $M^n$ possibilities for the sequence are: 

AAAA, AAAB, AABA, A**ABB**, ABAA, ABAB, **ABB**A, **ABB**B, BAAA, BAAB, BABA, B**ABB**, BBAA, BBAB, BBBA, and BBBB.

The sub-sequence ABB appears (highlighted in bold) 4 times out of 16, and in each of these four cases, it appears only once within the sequence. So the answer is 1/4 in this case. Note that for the sub-sequence AAA, the answer would be 3/16. 

In my case, $M$ is large (say, $10^7$) and $K$ is small (say $K=300$.) Both the sequence and sub-sequence are random in my case.