4. Each bag contains 5 small balls that are identical in shape, size, and material, numbered $1 \sim 5$. Without seeing the balls, one ball is randomly drawn from the bag, the number is noted, and the ball is then returned. Another ball is then drawn from the bag. The probability that the number on the ball drawn the second time is less than the number on the ball drawn the first time is $\qquad$
4. $\frac{2}{5}$.

All possible outcomes of drawing the balls twice are $5 \times 5=25$, among which, the number of cases where the number on the ball drawn the second time is less than the number on the ball drawn the first time is
$$
4+3+2+1+0=10 \text { (cases). }
$$

Therefore, the required probability is $\frac{10}{25}=\frac{2}{5}$.