Ok - what is the very lowest chance that a genuine champion fighter has to win against his most difficult opponent, assuming similar weight divisions. E.g. what chance does Frazier have against Foreman, what chance does Hatton have against Mayweather etc. Now, what chance does a non-champion live contender have against the same difficulty of opposition. E.g. what chance does Earnie Shavers have against Ali, what chance does Quarry have vs Frazier etc. Remember we are talking about the chance to win by any means - KO, cuts stoppage, split decision, injury etc.
I think what you're trying to ask is: what factors give a huge underdog a chance -- any chance -- at winning. In other words, what makes a big underdog occasionally successful. The answer to your question depends on two things. One, does the huge underdog have any particular trait -- any single trait that is special in what otherwise is an inferior fighting arsenal -- that gives him a chance. And second, does the favorite have any specific weakness that makes him vulnerable to the strength the underdog has. The most classic example of what I'm describing is a clubfighter who has a devastating punch. Overall, the clubfighter might be mediocre, but his punch may be great. Those kinds of guys have what's known as a "puncher's chance." If they swing for the bleachers all night long, sometimes they get lucky and kayo the favorite. But it takes luck. Sometimes you'll see mediocre clubfighters who have powerful right hands. If they are matched against a world class guy who has trouble blocking a right lead, for instance, then you may have the makings of an upset -- especially if the favorite is having an off-night. Just my two cents...hope my post isn't too long.