I think I'm right in saying too that Harry had spent some time looking at the photos he has of his parents and Sirius together - once he made the connection with their Best Man and Sirius Black. I felt his disappointment that one of the few people close to his parents had turned out to be this killer and probably suddenly realsing that he wasn't what he was said to be made him latch onto him as he would have done had he not been in Azkaban.
I think I'm trying to say he had almost been waiting for an excuse to really like him becasue his parents had.