Celeste Holm, Joyce Van Patten, and Tim O'Connor are two sisters and a brother named Lytton who are old money society people, but the money is drying up. They maintain a private museum that is a hobby that O'Connor thinks they can't afford. Holm is in our own little world, but Van Patten is a Margaret Thatcher like Iron Lady who is quite used to making sure she gets her own way. That museum is her life and she'll do whatever it takes to maintain it.
She works out a complicated scheme involving a less than trustworthy security guard to fake a robbery and fake his own death and then meet a real death when he goes to meet Van Patten at the museum. The guard was not the sharpest knife in the drawer. O'Connor hears the shot and Van Patten shoots him and makes it look like they killed each other.
Yet another well laid plan goes awry. Peter Falk was positively Monk like in his attention to the small details that unravel the whole plan. Van Patten has one weakness which Falk also plays on, Holm's daughter Jeannie Berlin is the daughter that should have been her's because Holm stole Van Patten's fiancé. It's a weakness Falk exploits to the fullest.
A pretty good episode for the Monk like detective with the raincoat.