Theory generally attributed to French mathematician and astronomer Pierre-Simon, Marquis de Laplace (1749-1827) in his Essai philosophique sur les probability (1820).
It says that the probability of an occurrence in a given situation is the proportion, among all possible outcomes, of those outcomes that include the given occurrence.
The main difficulty lies in dividing up the alternatives so as to ensure that they are equiprobable, for which purpose Laplace appealed to the controversial principle of indifference.
A related difficulty is that the theory seems to apply to at best a limited range of rather artificial cases, such as those involving throws of dice.
H E Kyburg, Probability and Inductive Logic (1970), ch. 3