When calculating the mean lifetime of an electron in a solid under the influence of a perturbation (for example electron-phonon interaction) we often apply Fermi's golden rule but the rate always has to be weighted by appropriate distribution functions (for example fermi functions). These take into account wether a given state is occupied of unoccupied and hence a candidate for the transition. Why do we need an "additional" probability for an unoccupied state? I mean, in the context of the Hilbert space the transition of a many-particle state to another isn't different from transitions between one particle states fundamentally. Isn't the probability already contained in the transition rate? In other words: The golden rule states: Given that the electron was in the state A (probability p(A)=1) what is the probability to find it in a continuum of states close to B at a time t? The rate is the time derivative of that probability. Isn't it redundant then to introduce a probability (1-P(B))? I hope I expressed myself clearly.