[SumZero]

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Ok, say you are trying to figure out a 3 way allin preflop equity calculation. Assume that we've already figured out the ranges of hands, and plugged them all into PokerStove. Hero is the middle stack. I want to find the probability of the shorty winning the main pot, but we win the side pot.
In other words, Pr(Hero wins sidepot | Short Stack wins main pot).
Given our hand and the ranges of hands, we have the following:
Pr(Shortstack wins main pot) = 28.6%
Pr(We win main pot) = 46.4%
Pr(Big stack wins main pot) = 25.0%.
If the short stack is not involved at all in what is entered into PokerStove, we have:
Pr(Hero beats big stack) = 66%
Pr(Big stack beats hero) = 34%.
Assume all chopping is lost in roundoff.
Is there a way to figure out what the above Probability is? If you need a tool like PokerStove (and you me to supply hand ranges), does PokerStove have all the functionality required to solve this problem?

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I'm not sure exactly what you're asking. If it is "What is the probability that I win the sidepot given the short stack wins the main pot?", the answer is equal to the percentage of times your hand beats the big stack in the hand, or 66%.
If you are asking what percentage of total outcomes have you losing the main pot to shorty but winning the sidepot, the answer is P(shorty winning) * P(your hand beats big stack) or .286 * .666 = 19.05%.
Hope this helps.

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The answer you give to the question is wrong. It may be a first order approximation of correct, but it isn't right.

You can partition the possible board cards into those that the short stack loses and those that the short stack wins. Looking only at boards when the short stack loses, you may have better, equal, or worse chances of winning against the other big stack as you'd have across all boards.

Simple contrived example:

Shorty has AK spades. Big stack has AQ clubs. Hero has red QQ. The two A's and three K's not in peoples hands are dead (folded by other players). Now the prob(Hero beats big stack) when shorty wins is ~100% (the only way he can not win when shorty wins is when shorty hits his flush and the board contains JT98 giving both other stacks a tie with the Q-high straight). The prob(hero beats big stack) when shorty loses is a lot, but is more like ~90% (as he loses any board with 3-or-more clubs and no Q-full house).