Given an Input string of N bytes where some bytes positions in the string are fixed/immutable (F Bytes) and rest of the bytes positions can contain any value as we want or are configurable/variable (V = N-F Bytes).
SHA256(SHA256(N)) = H (256 bits).
Now, Given an Input string of N bytes, the values of N, F, V and the positions which can change and which can't:
How do we calculate the probability/formula that for at least 1 assignment of values in V, the calculated H has k leading bytes as 0?
For eg: For a random input string of size N, N=80, F=40, V=40 (assuming the position information is also given) how do we know/calculate the probability that for at least 1 assignment of values in V first k bytes of H are 0?
I tried searching for some analysis on this but couldn't find any answer. Can someone please help?