In 1494, Fra Luca Paccioli released his work Summa de arithmetica, geometria, proportioni e proportionalita which was the first written text on probability.
The development of probability theory in the late 1400s was attributed to gambling when playing a game with high stakes, players wanted to know what the chance of winning would be. Probability and gambling have been ideas since long before the invention of poker.
In poker, the probability of each type of 5-card hand can be computed by calculating the proportion of hands of that type among all possible hands.