During the opening events of Philosopher's Stone, Sirius gave Hagrid his motorbike before going off to confront Peter Pettigrew. Then after leaving Harry on the Dursleys' doorstep, Hagrid said he would return the bike. It's never explained how he reacted when he found out Sirius had been accused of killing twelve Muggles, & had been taken to Azkaban as a result. Though it might be possible that he refused to believe it...
Then during the events of Chamber of Secrets, Hagrid is sent to Azkaban himself, having been suspected of being the culprit behind the attacks of many Muggle-borns. There's a 50% theory that he would've met Sirius there.
This leads us to wonder how less terrified he would've been when hearing the news that Sirius finally escaped Azkaban after serving twelve years there, & was currently on the run. It would've been less convincing if Hagrid had just told Harry that Sirius was innocent, & it was really Peter who had been Voldemort's spy, hence why neither him or Dumbledore had told him at all...