After his dissertation on “The concept of probability in the mathematical representation of reality” (Erlangen 1915), Hans Reichenbach elaborated a probabilistic theory of knowledge aimed at solving the problem of induction, first in the context of the Berlin Group of logical empiricism and after 1933 during his 5-years stay at Istanbul University. His innovative approach among the European empiricists at that time was based on a logic of probability, understood as a logic with a continuous scale of truth-values, in terms of which the two valued logic appears as special case. Reichenbach’s probabilistic theory of knowledge gave rise to vivid discussions in the mid 1930s, that led him to criticize harshly the “positivism” he associated with some representatives of the Vienna Circle, as formulated in his work Experience and Prediction (1938). Drawing on Reichenbach’s writings on the concept of probability and its epistemological significance, my presentation aims to clarify the idiosyncrasy of his reflections and their role in the early development of an analytical philosophy of science or, in Reichenbach’s words, of a “method of analysis of science” (wissenschaftsanalytische Methode).