The evidence against Santini was not conclusive. In many cases the evidence is thin and I imagine many murderers would get away with their crimes if they did not confess, sometimes stupidly though.

In this case I can 'forgive' Santini for confessing. Columbo has discovered that he is an ex Nazi, and soon the world will too. (We can debate if this could be proved since Santini destroyed the accusing letter.) I imagine Santini figured his life as he knew it was over, maybe that a US prison would be better than a foreign prison/

The evidence against Santini was not conclusive. In many cases the evidence is thin and I imagine many murderers would get away with their crimes if they did not confess, sometimes stupidly though.

In this case I can 'forgive' Santini for confessing. Columbo has discovered that he is an ex Nazi, and soon the world will too. (We can debate if this could be proved since Santini destroyed the accusing letter.) I imagine Santini figured his life as he knew it was over, maybe that a US prison would be better than a foreign prison/

I don't think the letter is necessarily proof of Mueller's identity (the state department will be able to confirm that) but it's proof that the victim intended to expose Mueller. So it's evidence of a motive.