Updating a Professor on Denying School Offer While considering my options, I reached out to a couple professors to inquire on their work. Ultimately, I've opted not to go to the school in question, though I would love to work with that professor in the future, if he is willing to be a co-advisor of sorts. While he has not explicitly said he is willing to work with me, I'd like to send an email informing him of my situation.

I ultimately decided to matriculate [elsewhere], but would love assist you in your future work if at all possible.

I feel this comes off as if I assume he is already willing, but am trying to express the opposite, where the burden of &quot;willingness to collaborate&quot; is on him? If that makes sense? Thanks in advance.
Your original phrasing would be interpreted incorrectly, as if you were the professor wanting to help a student. A note would be good, expressing thanks. You can also say that you would love to have the opportunity to work with them at some point in the future. But don't suggest, or even hint, at joint supervision at this point.
After you are in the new program you've selected and have had a chance to meet with your formal advisor, you could raise with them whether including the other professor in a formal way would be appropriate. There are two issues. First all three of you need to agree on a single problem direction and the actual advisor might have their own ideas about that. Second, there has to be a professional matchup that works for everyone, but especially the two professors. You don't know of any existing dynamics already in place and you don't want to step into a swamp inadvertently. The formal advisor might also just be unwilling to deal with additional complications, and might even be insulted that they weren't consulted first.
But even if the advisor isn't willing there is no reason to give up contact with the other professor informally. A semi-annual note, for example, on your progress will keep them in mind of you and possibly open opportunities in the future. But go slow initially.