Based on his own personal belief. Probabilities are a very useful way to precisely state the certainty of beliefs.
It means that if you offered him betting odds that it would happen, of less than 1:2, he would take it. And he would bet against it at odds higher than 1:2. Of course betting on the far future is impractical, because money might not be worth anything if it does happen, but in principle that's how these numbers can be interpreted.
Yes, I know where Bayesian epistemologists get their numbers.
The danger is that they then announce these numbers as if they have any real-world basis, and that they are taken as making a claim about objective reality.
There's no evidence I know that pulling a number out of your backside and running it through Bayes' theorem produces better results than just pulling the number out directly and running with it. Indeed, the real-world track record of LessWrong/MIRI (to bring this back to topical relevance) strongly suggests it's less effective.
It means that if you offered him betting odds that it would happen, of less than 1:2, he would take it. And he would bet against it at odds higher than 1:2. Of course betting on the far future is impractical, because money might not be worth anything if it does happen, but in principle that's how these numbers can be interpreted.