1. A deck of playing cards, excluding the big and small jokers, has a total of 52 cards. After shuffling, four people take turns to draw 13 cards each. The probability that the two red $\mathrm{A}$ s (i.e., the Heart A and the Diamond A) are in the same person's hand is $\qquad$ .
$-1 . \frac{4}{17}$.
Notice that, after the cards are shuffled, each person's cards are determined, i.e., the 52 cards are arranged in 52 positions. Let the four groups of card numbers be:
$$
\begin{array}{l}
1,5,9,13, \cdots, 49 ; 2,6,10,14, \cdots, 50 ; \\
3,7,11,15, \cdots, 51 ; 4,8,12,16, \cdots, 52 .
\end{array}
$$

Then the number of arrangements where the Ace of Hearts and the Ace of Diamonds are in the same group is $M=4 \mathrm{~A}_{13}^{2} \mathrm{~A}_{50}^{50}$.
Thus, the required probability is $P=\frac{M}{52!}=\frac{4}{17}$.