Easiest way....
- Create the path array and make sure it is not grouped.
- Select all and choose
Object > Transform > Transform Each...
- Decrease the
Horizontal Scale
percentage
- Make sure the 9-point origin is set to left center
- Tick the
Random
box....

Path lengths will be between whatever you use for the Horizontal Scale and 100%.
You can repeatedly tick and untick the Random
box to get different results each time, until you are happy. Then just click OK
.
Another method....
This method can be helpful is you need more control over the path lengths. While I use a random path here, the vertical path can be any configuration - a curve, specific insets, etc. Allowing you to "shape" the lengths more.
Draw a vertical path across the horizontal path array..

Choose Effect > Distort & Transform > Roughen...
And play with the settings to get a very random path.

Click OK
and then choose Object > Expand Appearance
to "bake in" the randomization on the path (making it a standard path).
- Select All and grab the Shape Builder Tool.
- Hold down the Option/Alt key and click-drag across one side of the random path.
This will remove all the stroke parts on that side of the random path.
Then select and delete the random path....

This will leave you an array of random length paths...

Of note: One may think that Pathfinder > Divide would be helpful here as opposed to Shape Builder. It is not. The Divide operation seemingly joins the random path segments to the horizontal array segments, connecting them. Meaning one would need to then manually go in and delete each and every connecting segment.