Total ways in which papers can be checked is equal $7^4$. Now, two teachers who have to check all the papers can be selected in ${}^{7}C_2$ ways and papers can be checked by them is $\left(2^4-2\right)$ favourable ways.

Thus, required probability

$=\frac{{}^{7}C_2\left(2^4-2\right)}{7^4}=\frac{6}{49}$