2. There is a $19 \times 19$ square chessboard. If two horizontal lines and two vertical lines are randomly selected, the probability that the enclosed shape is a square is $\qquad$ .
2. $\frac{13}{190}$.

Squares with side length 1 have $19^{2}$, squares with side length 2 have $18^{2}$, ... squares with side length 19 have $1^{2}$. Therefore, the total number of squares is
$$
1^{2}+2^{2}+\cdots+19^{2}=\frac{19 \times 20 \times 39}{6} \text { (squares) } .
$$

The required probability is
$$
P=\frac{19 \times 20 \times 39}{6} \div \mathrm{C}_{20}^{2} \mathrm{C}_{20}^{2}=\frac{13}{190} .
$$