Columbo's priors

By definition a person suspected by a detective is not just anybody, whose name was extracted at random from the list of citizens in the region where the crime was committed. Police does not like to lose time, money and reputation, if it does not have valid suspicions, and investigations proceed in different directions, with priorities proportional to the chance of success. The probabilities of the various hypotheses go up and down as the story goes on, and an alibi or a witness could drop a probability to zero (but policemen are aware of fake alibis or lying witnesses).

If we see Columbo loosing sleep following some hints, we understand he has strong suspicions. Or, at least, he is not convinced of the official version of the facts, swallowed instead by his colleagues: some elements of the puzzle do not fit nicely together or, told in probabilistic terms, the network of beliefs29he has in mind30 makes him highly confident that the suspected person is guilty.

Giulio D'Agostini 2010-09-30