The years spent in the hellhole that was Azkaban had taken their toll on Sirius Black. He had gone into the place a handsome vibrant young wizard, but now, now he was none of these things. He was older, as time will pass despite being innocent of any wrongdoing - he was haggard and gaunt, and the rags that passed as garments hung from his thin frame. He was tired, so very tired, and his mind was far from being sharp. It was a miracle he hadn't lost it, what with having been in this place for twelve long years. And he might have, had he not kept images of Remus safe in his heart, images that helped him through the interminably long nights. How he longed for his wolf, how he ached for him, wished to tell him he was innocent, he did nothing wrong. It was Peter - all Peter. But no one asked, and no one listened, and he had realized early on that he had been sent here for a reason, and there would be no escape.
But then came the rather fortuitous day when Cornelius Fudge-hole had come to the prison and Sirius had requested a copy of the paper from him - and if Sirius was such a desperate prisoner, why was Fudge so willing to give it to him? Regardless, then it was he realized that Peter lived and that Harry was in mortal danger. He had to escape, he simply had to, there was no help for it. So he did, by turning into Padfoot, so lean now that his ribs showed skeletally, and sliding between the bars, swimming across the North Sea to terra firma.
He traveled as Padfoot, because it was easier and because then he didn't have to think quite so much - plus it was safer. He took a short detour by Little Whinging, saw for himself that Harry was safe, but inadvertently frightened him, and last saw him getting on the Knight's Bus. He then began to make his slow and painful way to Scotland, toward the school, even as he wondered where his Remus was, and would he ever see him again.