The deceptively unassuming figure of Los Angeles homicide detective Lieutenant Columbo (Peter Falk), with his rumpled raincoat, cheap cigars, and seeming absentmindedness, might not call to mind the sprawling existentialist novels of Fyodor Dostoevsky. But Columbo’s ancestry can be traced all the way back to Porfiry Petrovich, the pesky, psychologically attuned investigator in Crime and Punishment.

Like that literary classic, the show that shares Columbo’s name functions as an inverted detective story, not so much a whodunit as a howcatchem. In each episode, we spend time with the murderer, soak up their milieu, and witness the commission of the crime. Only then does Columbo make his entrance onto the scene. From there, it’s an escalating battle of nerves between the dogged detective and the initially arrogant murderer.

While Rodion Raskolnikov, the tortured protagonist of Crime and Punishment, is an impoverished student who kills out of economic necessity...