Solution:
The total new employees $=6$
Therefore, they can be arranged in $6!$ Ways
$\therefore \mathrm{n}(\mathrm{S})=6 !=6 \times 5 \times 4 \times 3 \times 2 \times 1=720$
In 5 ways two adjacent desks for married couple can be selected that is $(1,2),(2,3),(3,4),(4,5),(5,6)$
In 2! Ways the married couple can be arranged in the two desks
In 4! Ways the other four persons can be arranged.
Therefore, the no. of ways in which married couple occupy adjacent desks

$\begin{array}{l}
=5 \times 2 ! \times 4 ! \\
=5 \times 2 \times 1 \times 4 \times 3 \times 2 \times 1 \\
=240
\end{array}$
Therefore, no. of ways in which married couple occupy non-adjacent desks $=6 !-240$

$\begin{array}{l}
=(6 \times 5 \times 4 \times 3 \times 2 \times 1)-240 \\
=720-240 \\
=480=\mathrm{n}(\mathrm{E})
\end{array}$

The required Probability $=\frac{\text { No. of favourable outcome }}{\text { The total no. of outcomes }}$
$=\frac{\mathrm{n}(\mathrm{E})}{\mathrm{n}(\mathrm{S})}=\frac{480}{720}$
$=\frac{2}{3}$