Question about the Appeal to Possibility

I was just wondering if the appeal to possibility is made only if someone assumes that an argument or assumption is correct simply because it's possible, or if it is only made when the backbone of the argument stems from it's possibility?

For example, a person I've had various discussions with commonly tries to convince me of several different conspiracies. They usually begin their argument with, "Isn't it possible that..." and usually doesn't give any evidence or anything. It'll just be something like "Isn't it possible that Donald Trump's candidacy is a plant by the democratic party to get Hillary Clinton elected?" I've heard a lot of arguments, some good, some bad, for why this statement is true or false, but it seems like the person is making the fallacy, because it seems as though they are indicating that the possibility is what makes it likely.

So the definition I use is: When a conclusion is assumed not because it is probably true, but because it is possible that it is true, no matter how improbable.

When someone says, "Isn't it possible that..." first you need to make sure that we know it is possible, and not just assume it is. I like to rephrase as "within the realm of known possibility." So if someone were to say, "Isn't it possible that invisible unicorns inhabit the earth?" we cannot agree with this because we don't know it is possible , we just don't know that it is impossible or not (there is a difference). If it passes the possibility test, then we need to ask the person if they are suggesting that just because it is possible, do they they think it is the most likely option . If they say yes, then they are committing a fallacy.