Given:
- A byte string $L$ of length $l$, sampled from a uniformly random distribution.
- A fixed byte string $S$ of length $s$, where $s$ $\leq$ $l$
- Window size $w$, where $w$ $\leq$ $s$
Find: The probability of $S$ existing in $L$, given that all windows from $S$ exist in $L$.
Example: $S$ = “abcd”, for a window size $w$ = 2, then all windows from $S$, $W_S$ = { “ab”, “bc”, “cd”}, find $P(S\ exists\ in\ L\ |\ all\ W_S\ elements\ exist\ in\ L\ )$