During the final chapters of Harry Potter and the Prisoner of Azkaban, Sirius Black escapes once again from Flitwick's office, while being guarded.
It is well known and established that you cannot Apparate within Hogwarts and moreover Sirius didn't have any wand with him to "magic" his way out. There needed to be outside help.
At the same time (well, around three hours before), Cornelius Fudge attended the supposed-to-be execution of Buckbeak. He saw the Hippogriff chained outside of Hagrid's hut and moments later, he (along with Dumbledore, Hagrid and the Committee members) saw that the Hippogriff had somehow fled.
How he didn't put two and two together and realize that Buckbeak was probably "used" to help Sirius escape from the seventh floor? He witnessed two nearly impossible escapes in three hours! I can't think that he was just unperceptive to realize this.