The given range is comprised of cards with a value between 3 and 7, inclusive, and there are 4 of each from the available suits. So there are 20 cards that fit the bill.
The probability of drawing 1 such card is
[tex]\dfrac{\binom{20}1}{\binom{52}1}=\dfrac{20}{52}=\dfrac5{13}[/tex]
