Assuming you are not asking for the historical origin, the uncontracted form of 'っこない' is 'ことはない'. Your sentence becomes お前には分かることはないでしょう
こと means here something like event or situation, so ' V + ことはない' (more) literally means that the situation where V happens is impossible. Hence, the construction means 'there is no way ...', as you already see.
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Among the posts linked in the comment, 逃げっこなし is basically the same (逃げることはなし) and the second っこ for reciprocal actions is different.
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ことない mentioned in other answers is possible but has different meanings. Either a simple negative sentence or meaning that someone goes beyond a reasonable limit. For example,
そんなに怒ることないでしょう - You don't have to get that angry (about such small matters)