Hanson is the most obvious answer, to me.
EDIT: Note, I don't think these people have given explicit probabilities. But they seem much less worried than people from the AI alignment community.
EDIT^2: Also, only the links to Hanson and Jacob's stuff have comparable detail to what you requested.
Bryan Caplan is one. Tyler Cowen too, if you take his claims of nuclear war being a much greater large-scale risk by far seriously and assign standard numbers for that. I think David Friedman might agree, though I'll get back to you on that. Geoffery Hinton seems more worried about autonomous machines than AI taking over. He thinks deep learning will be enough, but quite a few more conceptual breakthroughs on the order of transformers will be needed.
Maybe Jacob Cannell? He seems quite optimistic that alignment is on track to be solved. Though I doubt his P(doom) is less than 1%.
If you're willing to relax the "prominent" part of "prominent reasonable people", I'd suggest myself. I think our odds of doom are < 5%, and I think that pretty much all the standard arguments for doom are wrong. I've written in specific about why I think the "evolution failed to align humans to inclusive genetic fitness" argument for doom via inner misalignment is wrong here: Evolution is a bad analogy for AGI: inner alignment.
I'm also a co-author on the The Shard Theory of Human Values sequence, which takes a more optimistic perspective than many other alignment-related memetic clusters, and disagrees with lots of past alignment thinking. Though last I checked, I was one of the most optimistic of the Shard theory authors, with Nora Belrose as a possible exception.
Broadly, he predicts AGI to be animalistic ("learning disabled toddler"), rather than a consequentialist laser beam, or simulator.
Hmmm...
Ben Garfinkel? https://www.effectivealtruism.org/articles/ea-global-2018-how-sure-are-we-about-this-ai-stuff
Katja Grace? https://worldspiritsockpuppet.com/2022/10/14/ai_counterargs.html
Scott Aaronson? https://www.lesswrong.com/posts/Zqk4FFif93gvquAnY/scott-aaronson-on-reform-ai-alignment
I don't know if any of these people would be confident AI won't kill everyone, but they definitely seem to be smart/reasonable and disagreeing with the standard LW views.
https://www.rudikershaw.com/articles/ai-doom-isnt-coming
https://idlewords.com/talks/superintelligence.htm
https://kk.org/thetechnium/the-myth-of-a-superhuman-ai/
https://arxiv.org/abs/1702.08495v1
https://curi.us/blog/post/1336-the-only-thing-that-might-create-unfriendly-ai
https://www.popsci.com/robot-uprising-enlightenment-now
This one's tongue-in-cheek:
https://arxiv.org/abs/1703.10987
Update 1:
https://www.theregister.com/2015/03/19/andrew_ng_baidu_ai/
Update 2:
Katja Grace gives quite good counterarguments about AI risk.
https://www.lesswrong.com/posts/LDRQ5Zfqwi8GjzPYG/counterarguments-to-the-basic-ai-x-risk-case
When it comes to "accelerating AI capabilities isn't bad" I would suggest Kaj Sotala and Eric Drexler with his QNR and CAIS. Interestingly, Drexler has recently left AI safety research and gone back to atomically precise manufacturing due to him now worrying less about AI risk more generally. Chris Olah also believes that interpretability-driven capabilities advances are not bad in that the positives outweight the negatives for AGI safety.
For more general AI & alignment optimism I would suggest also Rohin Shah. See also here.
+ 1 for Katja Grace (even though their probability may be >1%, they have some really good arguments)
Ben Garfinkel in response to Joe Carlsmith: https://docs.google.com/document/u/0/d/1FlGPHU3UtBRj4mBPkEZyBQmAuZXnyvHU-yaH-TiNt8w/mobilebasic
Boaz Barak & Ben Edelman: https://www.lesswrong.com/posts/zB3ukZJqt3pQDw9jz/ai-will-change-the-world-but-won-t-take-it-over-by-playing-3
Here's Peter Thiel making fun of the rationalist doomer mindset in relation to AI, explicitly calling out both Eliezer and Bostrom as "saying nothing": https://youtu.be/ibR_ULHYirs
Francois Chollet on the implausibility of intelligence explosion :
https://medium.com/@francois.chollet/the-impossibility-of-intelligence-explosion-5be4a9eda6ec
Bounty [closed]: $30 for each link that leads to me reading/hearing ~500 words from a Respectable Person arguing, roughly, "accelerating AI capabilities isn't bad," and me subsequently thinking "yeah, that seemed pretty reasonable." For example, linking me to nostalgebraist or OpenAI's alignment agenda or this debate.[1] Total bounty capped at $600, first come first served. All bounties (incl. the total-bounty cap) doubled if, by Jan 1, I can consistently read people expressing unconcern about AI and not notice a status-yuck reaction.
Context: I notice that I've internalized a message like "thinking that AI has a <1% chance of killing everyone is stupid and low-status." Because I am a monkey, this damages my ability to consider the possibility that AI has a <1% chance of killing everyone, which is a bummer, because my beliefs on that topic affect things like whether I continue to work at my job accelerating AI capabilities.[2]
I would like to be able to consider that possibility rationally, and that requires neutralizing my status-yuck reaction. One promising-seeming approach is to spend a lot of time looking at lots of of high-status monkeys who believe it!
Bounty excludes things I've already seen, and things I would have found myself based on previous recommendations for which I paid bounties (for example, other posts by the same author on the same web site).
Lest ye worry that [providing links to good arguments] will lead to [me happily burying my head in the sand and continuing to hasten the apocalypse] -- a lack of links to good arguments would move much more of my probability-mass to "Less Wrong is an echo chamber" than to "there are basically no reasonable people who think advancing AI capabilities is good."