I would imagine that even if Geary didn't believe that he did it, just being caught in a bordello with a tied-up, murdered prosititute was enough to get him in their pocket. Given that Fredo had a good idea of Geary's favorite past-time, I'm sure it was easy enough to set him up so that he would be beholden to the Corelone Family. Notice how Geary's attitude in Cuba is so different than at Anthony's communion?