I personally will never buy used probes, unless you have the requisite equipment to test them, you may not realize there is a problem and end up confused by erroneous results. It is risky to buy irreparable used accessory when you don't know how it has been used, I liken used probes to some stranger's used underwear, no thank you.
In addition to the cable damage, your "shorter" probe is shorter because the pin is actually missing, or snapped off. The PP005 comes with two types of pins, a fixed pin, and a spring loaded pin. In your case, the other probe seem to have the fixed pin. You are also missing the ground pin, and the grabber extension.
The pin is replaceable, you can order part number PK102 for a set of probe accessory, about $40+ for a set.
I would consider getting the probe accessory kit if your probes are in better shape, but they both seem to be well used judging by the wear on the probe body. So if I were you, I would return them and buy a new set.
I have included a picture of what my PP005 looks like, you may want those missing accessories for a fully functional probe. I did not take picture of the probe ground spring, and the adjustment screw driver, which should also come with the probe set.