You'll find the answer at this link, oddly enough:
"kwassa (22,426 posts)
If you look at old "Columbo" episodes on tv, you will eventually see one where Columbo is wearing a baseball cap with the letters NFI on it. I've seen it.
My friend's brother, who was a friend of Peter Falk, wore such a cap onto the set one day. Peter asked him what NFI stood for. The brother said "No ******* idea".
Falk thought this hilarious. He asked for a hat just like it, and wore it on the show."
NFI has to do with his Alzheimer's Disease. It's the type "NFI" of Neurological Damage Peter Falk had.