 Hájek and Hitchcock 2016b is a short introduction to probability theory geared toward philosophical applications. Billingsley 1995 and Feller 1968 are two standard texts on probability theory. The entry for  interpretations of probability  includes a brief introduction to the formalism of probability theory, and discusses the various interpretations of probability. Galavotti 2005 and Gillies 2000 are good surveys of philosophical theories of probability. Hájek and Hitchcock 2016a includes essays covering the major interpretations of probability. 