In chapter 20 of Harry Potter and the Prisoner of Azkaban, it's made very clear that Peter Pettigrew needed a wand to use his animagus transformation and escape. However, one chapter earlier we learn that Sirius Black was using and reverting his animagus transformation inside of Azkaban. This gives us the absurd conclusion that Azkaban's prisoners have wands.
Clearly, something is wrong here. What's the solution? I could speculate that it can be done without a wand but Pettigrew, unlike Black, lacks the competence, but I'm hoping for something more solid and clearly present in the text.