3. There are 20 cards each inscribed with numbers $1,2, \cdots, 19,20$. They are placed in a box, and 4 people each draw one card. The two people who draw the smaller numbers are in one group, and the two people who draw the larger numbers are in another group. If two of them draw 5 and 14, respectively, then the probability that these two are in the same group is $\qquad$.
3. $\frac{7}{51}$ Detailed Explanation: Since two people have drawn cards numbered 5 and 14, the other two need to draw from the remaining 18 cards, which results in $18 \times 17$ possible scenarios. If the two who drew 5 and 14 are in the same group, there are two cases: (1) 5 and 14 are the smaller numbers, and the other two need to draw from the 6 cards numbered 15 to 20, which gives $5 \times 6$ possibilities; (2) 5 and 14 are the larger numbers, and the other two need to draw from the 4 cards numbered 1 to 4, which gives $3 \times 4$ possibilities; thus, the probability that the two who drew 5 and 14 are in the same group is $\frac{5 \times 6+3 \times 4}{18 \times 17}=\frac{7}{51}$.