Check it out ... Diddy smokes alongside a fan, named Chris Dayes (Christian Daigle), while listening to a song off a cellphone. Diddy, dressed in sunglasses, a baseball cap, and a Prince sweatshirt, looks totally at peace ... even though a grand jury indictment loomed over his head at the time.

The tipster tells TMZ ... the fan encounter occurred on the evening of September 9, when Chris approached the music mogul to pitch himself as a potential new artist.

We're told Diddy respected the guy's confidence and invited him to play one of his tunes ... taking the time to vibe and listen to Chris' track.

The tipster says Diddy was impressed with Chris' talent ... and noted he probably would've signed him if the circumstances were different -- hinting at his legal woes, which escalated with an arrest and an unsealed indictment this week.

Still, the tipster claims the Bad Boy Records founder was definitely in a "good mood" ... Diddy even wished Chris luck in his career before parting ways.

The rap mogul seemed to carry this energy into the rest of the week ... later spotted sunbathing in Central Park with his son, Christian "King" Combs, in the hours leading up to his arrest.

Again, Diddy put on an unbothered attitude ... seemingly unaware of the legal drama coming his way.

TMZ broke the story ... Diddy was arrested and taken into custody Monday evening when federal agents showed up at the Park Hyatt in midtown Manhattan, where he was staying.

U.S. Attorney Damian Williams later confirmed Diddy was booked following a sealed indictment filed by the Southern District of New York. The arrest came around 6 months after Diddy's Los Angeles and Miami homes were raided as part of an investigation into sex trafficking allegations.

On Tuesday, Diddy was charged with racketeering conspiracy, sex trafficking by force, fraud or coercion, and transportation to engage in prostitution. He was held without bail ... despite offering up a $50 million package.