Suppose there is a claim that outside the observable universe (assuming that there is an outside, other than that we don't know anything about outside) there exists a substance A. Can we conclude that substance A has a zero or close to zero percent probability of actually existing, or do we have to conclude that the probability of substance A existing is inconclusive and unkowable?
You either need to be more careful with your definition of "probability of actually existing," or at least use Bayesian statistics.
In Bayesian statistics, there is a factor which can be roughly translated as "knowedness." Thus it is valid to have some distribution (probability of true/false) with a 0 value for how known the value it. This leads to all sorts of interesting odd things like Jeffery's priors.
The other approach is being more careful with the wording. There is no actual scientific way to say "substance A has a % chance of existing" because that phrasing is ontological. It is a statement about the true universe, not what we know about it. An alternate phrasing would be "our empirical models suggest that the probability of A existing is very low."
This modeling step is critical. We have 0 information about whether this substance happens to exist on the dark side of the moon of a planet in another solar system. However, if our model of the universe suggests that most materials like substance A tend to be roughly evenly distributed across the universe, then we can sample the areas around us and do analysis.
In "pure" science, the way you'd do this is to create a null hypothesis that "substance A exists, but statistical anomalies account for why we haven't seen it yet." The alternative hypothesis is "substance A doesn't exist, or only occurs at some very low rate." You would make guesses as to the distribution of substance A (roughly uniform, in our case). You would then prove that it takes a great stroke of luck/bad luck to get a world where the distribution of substance A was just right to prevent us from detecting it.
Once you arrive at something like "there is a 0.01% chance that a random distribution of substance A would go undetected," you can say "we reject the null hypothesis" because we find it does a poor job of modeling our world. Then we get to claim the alternate hypothesis "substance A doesn't exist, or only occurs at some very low rate."
Note: we did not prove that hypothesis, we merely disproved the "prevailing" opinion that it exists, but random chance stopped us from observing it. This is a key difference in wording. Many wars have broken out between science and religion from individuals misinterpreting this path as "proving" substance A does not exist.