 using the Luchko's general fractional calculus, GFC, and its extension in the form of the multi-kernel general fractional calculus of arbitrary order, GFC of AO, a non-local generalization of probability is suggested. The non-local and general fractional, CF, extensions of probability density functions, PDFs, cumulative distribution functions, CDFs, and probability are defined and its properties are described. Examples of general non-local probability distributions of AO are considered. An application of the multi-kernel GFC allows us to consider a wider class of operator kernels and a wider class of non-locality in the probability theory. This article was authored by Vasiliy Tarasov.