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.
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.
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)