A seven digit number is formed using digits 3, 3, 4, 4, 4, 5, 5 ....

Digits $= 3, 3, 4, 4, 4, 5, 5$

Total $7$ digit numbers $= \dfrac{7 !}{2 ! 2 ! 3 !}$

Number of $7$ digit number divisible by $2$

$⇒$last digit $= 4$

Now $7$ digit numbers which are divisible by $2$

$= \dfrac{6 !}{2 ! 2 ! 2 !}$
Required probability $= \dfrac{\dfrac{6 !}{2 ! 2 ! 2 !}}{\dfrac{7 !}{3 ! 2 ! 2 !}} = \dfrac{3}{7}$