Sirius did not escape Azkaban in order to kill Peter Pettigrew.
He had known about Peter for twelve years. Sirius only escaped when he realized Peter Pettigrew was near Harry. And when he did escape, the first place he went was Privet Drive, just to get a look at his godson.
It was always about protecting Harry. The possible revenge was just a perk.
Where did you go? Round your dad’s. I was always welcome at the Potters’.
If you want to know what a man’s like, take a good look at how he treats his inferiors, not his equals.
HARRY POTTER MEME » [5/9] characters: Sirius Black
character posters: sirius black
clever as the devil and twice as pretty
…he was always sad