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
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,
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.