Answer
Each of the cables is stretched by $\frac{\Delta L}{9}$
Work Step by Step
$Y = \frac{F/A}{\Delta L/L}$
$Y$ is Young's modulus
$F$ is the force
$A$ is the cross-sectional area
$\Delta L$ is the change in length
$L$ is the original length
We can find an expression for $\Delta L$ before the cable is cut:
$\Delta L = \frac{W~L}{A~Y}$
After the able is cut into three pieces, each cable supports a weight of $\frac{W}{3}$. We can find an expression for $\Delta L'$:
$\Delta L' = \frac{(W/3)~(L/3)}{A~Y}$
$\Delta L' = \frac{1}{9}\times \frac{W~L}{A~Y}$
$\Delta L' = \frac{1}{9}\times \Delta L$
$\Delta L' = \frac{\Delta L}{9}$
Each of the cables is stretched by $\frac{\Delta L}{9}$.
