Of course, the attenuator in an oscilloscope must also be frequency-independant. Moreover, the input resistance and capacitance must always be the same. Otherwise, we need to re-adjust our HF probe for every attenuator.

The picture above shows two attenuators. The top one devides the voltage by 10, the bottom one by 100. Let's first take a look at the top one.

R103 is parallel-connected to the input resistance (RIN) of the scope. So the total resistance is: 1/R = 1/RIN+1/R103, so R = 100k. R102 is 900k, which means that the attenuation is 10, and that the input resistance remains 1MΩ.

C103 is parallel-connected to the input capacity (CIN) of the scope. The total capacity will be 47p + 30p = 77pF. VC102 must be adjusted to 77p∙100k/900k = 8.56pF. The new input capacity is 7.7pF. To make it 30pF again, VC101 must be set to 30p - 7.7p = 22.3pF.

For the bottom attenuator we can follow the same route. R105 makes RIN 10.1k//1M = 10k. R104 is 990k, so the attenuation is 100. C105 makes CIN 82p + 30p = 112pF. VC104 must be set to 112p∙10k/990k = 1.13pF. The input capacity is now just 1.12pF. VC103 must therefore be adjusted to 30p - 1.12p = 28.88pF.