Sources with direct knowledge tell us that Kim's just-announced role for this Ryan Murphy-led show -- which is going to air on Hulu -- is inspired by the famed Laura Wasser ... who's well-known in L.A. as being the go-to celebrity divorce lawyer for all the big shots.

In fact, Laura actually handled Kim's divorce from Kanye ... but her list of celeb clients is long and extensive, going well beyond the Kardashians. Some of the biggest stars who've retained her over the years include Kris Jenner, Ariana Grande, Ryan Reynolds, Angelina Jolie, Kevin Costner, Britney Spears, Heidi Klum and Christina Aguilera ... just to name a few.

As far as what the show will be about ... well, Deadline says it's gonna be a "sexy adult procedural" that covers her career as a hot-shot lawyer working in Los Angeles. The outlet reports that there's a big series commitment from the streamer ... although it's unclear how many episodes it'll be.

Kim will be heading a fake all-female law firm in the show, and it's being written by Jon Robin Baitz and Joe Baken. Of course, Murphy is EP'ing. Deadline reports the trio pitched Kim and Kris on this show ... and they both were apparently all in on it right away.

The fact Hulu picked this up is also no surprise considering they already air "The Kardashians." Word is, they signed on right in the pitch room and committed to a straight-to-series play. Of course, this comes on the heels of Kim's recent Netflix movie ... for which she'll also star and produce. Seems like Hulu wanted to mark their territory a bit!

Kim's already got some experience with Murphy ... she just acted in his latest season of 'AHS' and did pretty well. Her acting career is well on its way now -- what a time.