Let (0, 9 be two states of a *-algebra and let us consider representations of this algebra R for which o and p are realized as vector states by vectors x and J’. The transition probability P(w, e) is the supremum of all the numbers 1(x, y)l* taken over all such realizations. We derive properties of this straightforward generalization of the quantum mechanical transition probability and give, in some important cases, an explicit expression for this quantity.