Randomly pick one. The remaining papers will have one matching letter and three pairs of different letters. This means that for the first pair there is a 1 in 7 chance of them matching.

For the second pair, the same reasoning applies except that there are now only two pairs of different letters so there is a 1 in 5 probability of them matching.

The third pair has a 1 in 3 chance and if all 3 of these pairs match then the last pair must also match.

The total probability is worked out by multiplying all of these together, so it is 1 in (7x5x3x1) or if you want to be really technical, 1 in 7!!, which works out to be 1 in 105.