Is P(a|b) = ( P(b) * P(b|a) ) / P(b) more true when the probabilities are from a binomial distribution as opposed to poisson, or am I just confused and it doesn

Is P(a|b) = ( P(b) * P(b|a) ) / P(b) more true when the probabilities are from a binomial distribution as opposed to poisson, or am I just confused and it doesn't matter.