For me, the point is that Columbo, always the keen observer of psychology, knows that Santini's ego is his weakness. Columbo knows that Santini would never allow himself to be (seemingly) defeated in front of an audience -- even at the expense of incriminating himself in a murder case.
I do love that echange of "looks" (all of the comments here are good interpretations) in this "I knew you could do it" scene.
Just to further expand on my previous theory: He (Santini) could only know what kind of lock it was once he started picking it. As he did, he realized it was the same type of mechanism used in Jerome's door. That's when he realizes what Columbo is pulling on him, thus 'the look'.