Four cards are successively drawn without replacement from a deck of 52 playing cards. What is the probability that all the four cards are king?

Let ${E_1},{E_2},{E_3}$ and ${E_4}$ are the events that the first, second, third and fourth card is king, respectively.

$\therefore$ $P\left( {{E_1} \cap {E_2} \cap {E_3} \cap {E_4}} \right) = P\left( {{E_1}} \right) \cdot P\left( {{E_2}/{E_1}} \right) \cdot P\left( {{E_3}/{E_1} \cap {E_2}} \right) \cdot P\left[ {{E_4}/\left( {{E_1} \cap {E_2} \cap {E_3} \cap {E_4}} \right)} \right]$

$= \frac{4}{{52}} \cdot \frac{3}{{51}} \cdot \frac{2}{{50}} \cdot \frac{1}{{49}} = \frac{{24}}{{52 \cdot 51 \cdot 50 \cdot 49}}$

$= \frac{1}{{13 \cdot 17 \cdot 25 \cdot 49}} = \frac{1}{{270725}}$