That is as yet indeterminate. It may be the EHT supply that is faulty, the probe, or the discharge tube. Do not overthink the analysis.
1. You can test the CRO with against it's reference, and other sources.
2. You can test the probe with the working CRO on AC voltage. Does the probe have an AC/DC switch?
3. You can then test the EHT supply with all previously tested items.
4. Lastly you can test the discharge tube.
At any point you may need to back-track, or to check cables and connections.
The 1k resistor from ground to "ground electrode of device" is probably there to conduct leakage currents, to prevent voltages floating and breaking down the insulation. I do not have the schematic diagram of your circuit, or know which particular "device" you might be referring to.
You can post a link, or attach a picture to a post.