Harry Potter and The Pest of Azkaban

Draco Malfoy was thrown into Azkaban with his parents after the downfall of the Dark Lord. Six months later, when he's settled in as much as one can settle in when they're living on an island of misery and death, a new, surprising inmate takes up residency in the cell across from him. What is Harry Potter doing in Azkaban and Why does he seem convinced that he can get out?