It's been a few years since I watched this episode, but I always thought the evidence was weak against Adrian; however, the prospect of his life with his secretary (Julie Harris?) made him confess to his crime.
Yea it's one of the least credible episodes but that's never been my criteria for an enjoyable Columbo. To me, it's all about the interaction between the villian and Columbo. In this regard, i've never understood the sympathy Adrian Carsini draws, from both viewers and Columbo. The man was a selfish indulgent ****** who squandered the family fortune, half of which was rightfully his brothers, and murdered him in order to continue to do so. His cold relationship with his secretary is another clue to his lack of any real emotion towards anyone but himself. I just don't see much likable about the guy. I do like the episode a lot though, because in spite of the incongruous treatment he recieves from Columbo at the end, it's an interesting character study of this type of person.