  Triggered by a recent interesting New Scientist article on the too frequent
incorrect use of probabilistic evidence in courts, I introduce the basic
concepts of probabilistic inference with a toy model, and discuss several
important issues that need to be understood in order to extend the basic
reasoning to real life cases. In particular, I emphasize the often neglected
point that degrees of beliefs are updated not by `bare facts' alone, but by all
available information pertaining to them, including how they have been
acquired. In this light I show that, contrary to what claimed in that article,
there was no "probabilistic pitfall" in the Columbo's episode pointed as
example of "bad mathematics" yielding "rough justice". Instead, such a
criticism could have a `negative reaction' to the article itself and to the use
of Bayesian reasoning in courts, as well as in all other places in which
probabilities need to be assessed and decisions need to be made. Anyway,
besides introductory/recreational aspects, the paper touches important
questions, like: role and evaluation of priors; subjective evaluation of Bayes
factors; role and limits of intuition; `weights of evidence' and `intensities
of beliefs' (following Peirce) and `judgments leaning' (here introduced),
including their uncertainties and combinations; role of relative frequencies to
assess and express beliefs; pitfalls due to `standard' statistical education;
weight of evidences mediated by testimonies. A small introduction to Bayesian
networks, based on the same toy model (complicated by the possibility of
incorrect testimonies) and implemented using Hugin software, is also provided,
to stress the importance of formal, computer aided probabilistic reasoning.
