The verdict

In summary, these are our reasonable beliefs that a person would have behaved that way producing that sequence of actions ($ {\cal A}$), depending on whether he was a killer ($ K$) or not ( $ \overline K$), maintaining or not self-control ($ SC$/ $ \overline{SC}$):
$ P({\cal A}\,\vert\,\overline K, I) = 0$
: this is the main point, that makes the hypothesis innocent definitely impossible.
$ P({\cal A}\,\vert\,K\cap {SC}, I) = 0$
: a cool murderer would have never reacted that way.
$ P({\cal A}\,\vert\,K\cap {\overline{SC}},I) > 0$
: this is the only hypotheses that can explain the action. Here `$ >0$' stands for `not impossible', although not necessarily `very probable'34. Let us say that, if Columbo had planned his stratagem, based on a bluff, he knew there were some chances Galesco could reacted that way, but he could not be sure about it.
Given this scenario, the `probabilistic inversion' is rather easy, as only one hypothesis remains possible: that of a killer, who even had lost self-control.

Giulio D'Agostini 2010-09-30