I agree with the analysis above. Miss Abigail was almost caught red handed trying to throw the keys into the sea. Wouldn't that leave anyone flustered and unsettled. She knew somethng Columbo didn't and he was right there unexpectedly. So she made a BIG mistake by saying she had found the keys. It merely confirmed Columbo's suspicions and affirmed his theory she was the murderer. Perhaps she ought to have walked along the same beach in the first scene and buried them in the sand!!!! Discretly of course and miles away from Columbo!

This seems to be an occurring theme throughout the series, the killer helping Columbo with a clue he needs only to hang themselves in the process. Hayden Danzinger and the gloves is another good example.