A x10 oscilloscope probe means that the voltage is attenuated 10 times?
The 10x attenuation assumes that the oscilloscope has an input impedance of 1 MΩ. The probe itself has a 9 MΩ resistor in series (along with a capacitor for transient compensation). The actual voltage seen by the input of the oscilloscope is 1/10th of the voltage between ground and the probe tip. 

While a 35V input is pretty low, I have seen the voltage rating of a (passive 10x) oscilloscope probe be lower than the attenuation factor times the voltage rating of the oscilloscope. I had a 10x probe rated for 400V, but the oscilloscope input was rated for 100V.