Please excuse me if this topic has been discussed ad nauseum, but I am curious as to how Don Corleone was able to figure out with absolute certainty that Barzini was behind the fighting between the families and Sonny's death.

Did he do something in particular at the meeting since Vito had mentioned to Tom "I didn't know until this day that is was Barzini all along."?

It seems to me that since Vito had the politicians in his pocket, he held the power and not Barzini.

Any thoughts would be appreciated.