Each bridge hand receiving exactly one ace

A shuffled $52$-card deck is dealt into four hands of $13$ cards each. What is the probability that every hand contains exactly one of the four aces?

$\tfrac{2197}{20825}\approx0.105$. Place the aces one at a time into the $52$ positions: the second ace must avoid the first ace's hand ($\tfrac{39}{51}$), the third must avoid two hands ($\tfrac{26}{50}$) and the fourth three hands ($\tfrac{13}{49}$). The product is $\tfrac{39\cdot26\cdot13}{51\cdot50\cdot49}$.