Ex - Post Algorithmic Probability

Classical Probability theory is badly equipped to compute the probability of unique events, as it lacks the means to determine the relevant class to which the event belongs. Algorithmic Probability is designed to deal with individual events. It computes the chances that a given event will be output by a universal computing machine fed with random programs. This definition, however, fails to detect what makes an event noticeable. All non-trivial events are therefore assigned probabilities close to zero. The definition of probability proposed in this paper determines remarkable aspects of a situation ex post (after the fact). Contrary to Algorithmic Probability, it computes probability by considering a difference in complexity. Improbable situations are situations that are simpler to describe than to generate. This definition of probability leads to a new notion of information.