Many criminals made the mistake of underestimating Lieutenant Columbo, a homicide investigator with a crumpled trench-coat and a beat-up car, who certainly acted as an incompetent bumbler.
But he was so polite to every suspect, and he talked so much about his wife (who we never got to see on any episode, but who many believe later had her own show, starring Kate Mulgrew, later of Star Trek: Voyager fame) that he lulled even the shrewdest murderer into a false sense of security.
And although the audience had witnessed the murder in the beginning of each episode, it was still a surprise to see what mistakes the killers had made during the seemingly perfect murder.