One day he's tasked with escorting four scientists to the mayor's office -- the Ghostbusters. The reason? As Al himself states, "The whole island's going crazy." That's your "No s**t, Sherlock" assessment of what happens after the EPA and Agent Walter Peck shut off containment in the Ghostbusters' basement, releasing a monumental amount of pissed-off spirits in Manhattan.
It's safe to assume Powell hears at least part of what Egon and crew are explaining to each other and the assorted men in lock-up about what's happening, and that includes a Sumerian god showing up to destroy humankind. That's a hell of a lot of crap to take at work. And of course you'd never believe it, unless you were in New York at the time, where walls are bleeding and the dead are routinely covering people in ghost snot. Al Powell would have no reason not to believe what these four men, summoned by the mayor himself, are saying.
If we know nothing else about Powell, we know he's a talkative man -- it's a key aspect of his character in Die Hard (we'll get to that shortly). So he probably would have chatted with the Ghostbusters and got their side of what was happening, including the layman's explanation Egon already offered earlier in the film, aka the Twinkie.