An episode with old ladies and murder.

Can anyone identify the episode I remember from about 60 years ago?

It involved old ladies and murder.

As I remember there was a scene where a detective accused an old woman of the murder. She had found a dead body and in shock dropped the tray she was bringing tea in. But the detective said that the broken china tea service was the cheap set and not the more expensive set she usually used. The detective deduced she dropped the tray to pretend she was surprised and shocked by the dead body but actually already knew the victim was dead so used the cheap china instead of the expensive china.

So naturally the detective should have just arrested the old lady then and there.

But I also remember in the final scene they were driving to the house where the person they suspected lived - and perhaps to prevent another murder - and when they got there it was burning to the ground.

So how many people lived in the house? The victim, the one who I remember being exposed as the (or a) murderer, and the one who burned down the house (unless the house was burned by a neighbor or a mob with pitchforks and torches). And maybe the person who burned the house down burned it to kill a fourth resident, or destroy evidence of that murder.

Or maybe it wasn't a private house but an old ladies home with dozens of residents who had been dying at an unusual rate lately.

Or do my memories confuse two separate episodes?