Near the end of PoA, Harry and Hermione are making their way back to the hospital wing after their adventure with the time turner:

Their footsteps died away. Harry and Hermione waited a few moments to make sure they’d really gone, then started to run in the opposite direction. Down one staircase, then another, along a new corridor — then they heard a cackling ahead.

“Peeves!” Harry muttered, grabbing Hermione’s wrist. “In here!”

They tore into a deserted classroom to their left just in time. Peeves seemed to be bouncing along the corridor in boisterous good spirits, laughing his head off.

“Oh, he’s horrible,” whispered Hermione, her ear to the door. “I bet he’s all excited because the dementors are going to finish off Sirius. . . .” She checked her watch. “Three minutes, Harry!”

They waited until Peeves’s gloating voice had faded into the distance, then slid back out of the room and broke into a run again.

“Hermione — what’ll happen — if we don’t get back inside — before Dumbledore locks the door?” Harry panted.

“I don’t want to think about it!” Hermione moaned, checking her watch again. “One minute!”

Hermione has a poor opinion of Peeves (no wonder) and assumes that he is in good spirits because they are going to give the Dementor’s Kiss to Sirius. But soon after this Snape returns to the hospital wing, enraged that Sirius has escaped. Peeves must have overheard the revelation that he was gone and zoomed ahead, cackling with the news that a fellow rule breaker had escaped the authorities. Compare with when Fred and George Weasley left Hogwarts for good:

“STOP THEM!” shrieked Umbridge, but it was too late. As the Inquisitorial Squad closed in, Fred and George kicked off from the floor, shooting fifteen feet into the air, the iron peg swinging dangerously below. Fred looked across the hall at the poltergeist bobbing on his level above the crowd.

“Give her hell from us, Peeves.”

And Peeves, whom Harry had never seen take an order from a student before, swept his belled hat from his head and sprang to a salute as Fred and George wheeled about to tumultuous applause from the students below and sped out of the open front doors into the glorious sunset.