Create a probability formula relating to blockchain Proof-of-Work systems

Create a probability formula relating to blockchain Proof-of-Work systems: Given: 1. a hash of N bits, 2. a 'difficulty' of L leading zero bits, 3. a matching hash (generic solution S) is found on average in M minutes. (by varying a part of the input data, nonce) Someone selects one predetermined hash fitting the above requirements and searches only for this hash (thus all bits known in advance). What is the probability P that one can find that specific hash before anyone finds a generic solution? I need this formula for calculating P as a Latex math (source) formula with some basic why / how clarification.