Appeal to extremes? Absurdity?

I just had a situation come up where a person said "But you can't be 100% sure  that there is no possibility of this"
well, no, I can't be sure that the earth won't get hit by an asteroid and we're all wiped out tomorrow either, so they're perhaps factually correct, but I just think that it's an absurdity to require me to use that much precision and write 99.999999%
Is there a good way of dealing with this?

You ask how to deal with the proposition: “But you can't be 100% sure  that there is no possibility of this.” I see this normally as a tactic to end a discussion or the Fallacy of Diversion to divert the discussion to another subject.

I think it is essential to note that we can never be absolutely certain of anything other than metaphysical axioms, so we must assign a value to any proposition based on the available evidence. To dismiss a proposition on the basis it hasn’t been proven beyond all possible doubt is fallacious reasoning if one seeks knowledge. We can, however, attain an epistemological certainty, which, loosely restated, means beyond a reasonable doubt, while keeping our minds open to additional evidence or a different interpretation of available evidence.

Knowledge is the correct identification of the facts of what exists, of reality. This is the easiest definition to grasp that I have encountered. This is an important concept to keep in mind. For example, suppose you hold a belief that does not correctly identify the facts of reality. In such a case, that particular belief is not knowledge. The purpose of the scientific method is to correctly identify the facts of reality, but beyond this discussion.

How to deal with it is a different issue. Do not confront the person with facts and logic and all that stuff. Instead, do the Boghossian approach. 

In my experience, people never change their beliefs by being punched in the head with facts. Most people believe what they believe because they want to believe what they currently believe. Facts are not important. Michael Shermer made this addition to Cognitive Dissonance Theory in his book, “Why People Believe Weird Things.” So, if your goal is to change another person’s belief, I think you must use a different approach.

Peter Boghossian suggested a strategy to change a person’s belief. To be successful, he said the person whose belief you want to change must reconsider how he arrived at the belief under discussion. If your goal is to change his mind, as distinct from pontificating (which is better done in front of a mirror), then you need to get him thinking about how he arrived at the belief.  

Boghossian’s book, “How to Have Impossible Conversations,” is an excellent manual on how to do this.

 I’ve come to a different conclusion and I’m having a hard time understanding where you’re coming from. I assume you must know some things about this that I don’t. Could you tell me more about where you’re coming from on that so I can understand better?      

The more ignorance you admit, the more readily your partner in the conversation will step in with an explanation to help you understand. And the more they attempt to explain, the more likely they are to realize the limits of their knowledge and epistemological errors made along the way.

If you ask someone a direct question and he obfuscates or refuses to answer, ask him to ask you the same question, and you answer it. Other Boghossian suggestions:

 “That’s an interesting perspective. What leads you to conclude that?”

 Say, “I’m skeptical,” not “I disagree.”

I think the answer previously given is not correct.   Appeal To Possibilities is where it is concluded that something is true because it is possible.  That was not the question asked, which was whether a conclusion should be rejected because it is possible that it is not true.

The question is a good question and goes (again) to the distinction between validity in Deductive Logic and strength in Inductive Logic.  Inductive Logic only requires that the conclusion probably follow from the premises, and if there is only an infinitesimal chance that the Earth will be destroyed by an asteroid in the next 24 hours, then it is a strong argument to conclude that it won't.  Only deductive arguments require 100% certainty for validity, and that is because the form of the conclusion follows with necessity from the form of the premises.   Deductive arguments never say anything new about the outside world; they only say what you can infer from the form of the premises.  

Whether confusing a strong Inductive argument with the need for deductive certainty is a named fallacy-I'm not aware that it has been named.

Depends on what they meant. I'd need to see the context to be sure, but I can make three educated guesses:

"There's always a possibility you're wrong" - just a factual statement, and it's probably correct (since most arguments are probabilistic, or inductive).

"You can't be 100% sure you're right, therefore you're wrong" - non sequitur as it doesn't follow that someone not being certainly right means they have to be wrong. There's a much greater probability that the person is right, so that should be what we focus on.

"There's a possibility you're wrong and I'm right, therefore I'm right" - appeal to possibility since the claim is asserted as true based on mere possibility, rather than evidence.

Perhaps, the most insidious fallacy of them all: the appeal to possibilities.