The story, as told in a new Hulu documentary about Shyne, goes like this ... Diddy was on his way to court to learn the verdict in his shooting case when he had his driver make a pit stop in Central Park.

A man was waiting for Diddy and when Diddy approached the guy, Diddy dropped to his knees ... and smoke started swirling around Diddy. The bodyguard, Gene Deal, thinks the burning substance was sage.

Deal says the guy appeared to have a Bible as he started praying and placing his hands on Diddy ... before telling Diddy to grab a white bird from a cage. Diddy threw the bird in the air and it dropped to the ground like a brick.

The bodyguard says that was the end of the ritual ... the bird was dead and Diddy walked away.

Hours later, Diddy was acquitted on attempted bribery and weapons possession charges ... a huge relief, considering he was staring down 15 years in prison if convicted.

Shyne, on the other, hand was found guilty of assault, reckless endangerment and criminal possession of a pistol ... with Diddy's former Bad Boy artist being sentenced to 10 years behind bars.

Deal makes the bird sacrifice claims in "The Honorable Shyne" ... a new Hulu documentary about Shyne that's dropping today.

Shyne says Diddy made him the fall guy in the case and claims it was all part of some "demonic" plot by Diddy ... allegations Diddy denies.