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Master equation for catylist and substrate binding?

I recently asked this on Biology.SE, and need to start with the master equation for the reaction: $$E+S\rightarrow ES$$ Where $E$ is our enzyme and $S$ the substrate to get a probability density function for the binding time of a substrate with one specific enzyme to be: $$f(t)=k[S]e^{-k[S]t}$$ I have read up on master equations, but really have no idea where to start in this derivation, any help would be appreciated?