The variable C on the probe is to compensate for the tolerance the dielectric shunt capacitance of the 10:1 probe.
The first diagram is amplified but shows the effect of excessive differentiation from high variable C in series to the 9C cable shunt capacitance. They intensionally use higher impedance probe coax and thus higher L/C or lower C for a given length to reduce the size of the tiny variable C/9. Thus the total probe load is the scope impedance x 10 with ~C/10 with both C’s in series to the load. You get C/10 by = (C/9 * C ) / ( C/9 +C) = C-probe for DSO input= C
Thus 1/(9+1) ratio of C’s is called a 10:1 capacitance transformer just like inductive turns ratio transformers is for low frequency, thus is just for high frequency balancing with the R ratios of the same in parallel with C’s. Except the probe is 9M and the DSO is 1M also with some capacitance. So the probe must be rebalanced if used on a different scope using to provided test port with a square wave.
Another variable is the ground lead inductance which will cause ringing near 20 MHz assuming ~0.5 to 1 nH were lead length resonating to probe coax capacitance .
- This requires you to remove the ground clip and Probe clip and use a spring probe over the tip and barrel of the probe with 2 wire pins near signal + gnd in order to get the full BW of scope whether it is 50, 100, 200, or >1GHz
It gets a bit more complex than this as explained by TEK and HP on probe designs but essentially you get a high impedance matched 10M to 1MOhm broadband voltage divider.