Columbo invented the "rope-a-dope."
The criminals he pursued were always egomaniacs with a lot of skill and success in one area; they typically thought their narrow expertise made them invincible. Columbo fed their egos and generally acted like a harmless teddy bear until it was too late.
One of he beautiful things about the Columbo concept was that the villians could be actors of marginal ability... often Levinson and Link used greats who were a little past their prime. Their slightly rusty acting skills were perfect for a criminal that was having trouble hiding the truth, not quite sure how they would have reacted to Columbo if they hadn't done the crime. At least one Columbo (the one with the orchestra conductor who murdered someone in his home) was directed by Steven Spielberg.
My favorite is called "Any Port in the Storm," in which Donald Pleasance was a vintner who murdered his brother.
The one with Leonard Nimoy as a surgeon who deliberately used the wrong stitches, and kiiled the lady that discovered it was the only episode when Columbo actually displays a bit of righteous temper!
He did! The supreme master.