Most probes are modular to some degree. Some dismantle completely.
You could detach the cable from the probe and swap with another to find where the fault is.
Some tips unscrew, insulation tube on tip slides off, cable plugs in, BNC compensation unplugs etc. etc.
Have a "play" with the faulty one first to understand how they are put together.
Check reference (GND) continuity from tip to BNC.