In his apology for "personal knowledge," Michael Polanyi describes probability as expectation, and surprise as the inverse of probability. (cf information)
He points out that a probability statement cannot be contradicted by the events. Contradiction can only be established by a personal act of appraisal which rejects certain possibilities as being too improbable to be entertained as true. (pp 20 - 24)
When the when the expectations based on a statement of probability are repeatedly disappointed, we begin to doubt the statistical statement. Even then, expectations based on probability statements are only gradually weakened.
In his study of The Emergence of Probability, Ian Hacking documents the persistence of the medieval meaning of probability as the approvability of an opinion. According to Aristotelian canons, scientia was distinguished from opinio, which was the realm of probability rather than certainty. People provided the basis for probability, not the evidence provided by things. In fact, according to Hacking, there was no concept of evidence. Opinion depended upon the approval of authority, especially the testimony of ancient books.
For Renaissance hermetics like the physician Paracelsus, the sign was a matter of reading the True Book of nature, based on a theory of similarity. Nature could confer evidence, but only in the old way of reading and authority. (p.44) The development of the concept of evidence required a transformation of the concept of the sign, from the "signature" or true name of things, to an expression of internal evidence. This transformation would enable probability statements to become assertions of "propensity" or tendency, and for the "calculus of of frequencies" to be assimilated to notions of epistemic probability and non-deductive inference.
Hacking's account follows Michel Foucault's description in Chapter 2 of The Order of Things (Les Mots et les Choses) in the changing epistemè of the late sixteenth century and the emergence of classicism. For Foucault, the figures of knowledge were organized by the forms of ressemblance: convenentia, "that brings things together and makes adjacent things similar", aemulatio, which "enables things
In looking at the sudden emergence of the concept of probability around 1660, Ian Hacking draws attention to the duality of probability, having to do with both stable frequencies and with degrees of belief, bot h aleatory and epistemological. For Hacking, this particular concept of probability arose within certain preconditions, within a "space of possible theories about probability." (p.9)
For one mathematical treatment of probablilty, see entropy.