A typical x10 probe schematic is shown below, when connected to a typical scope input. The key difference between this schematic, and the schematic of the article mentioned by the OP, is the presence of C1 at the probe tip. C1 compensates for drop-off in frequency response by providing a low-impedance path for high-frequency signals.

simulate this circuit – Schematic created using CircuitLab
Description of the Schematic:
R1 & R2 form a divide-by-10 voltage divider for DC, but the AC response of is determined by the three capacitors:
C1: This is usually a fixed-value high-voltage capacitor with low inductance and low dielectric loss.
C2: This is an adjustable capacitor, the one you tweak to "compensate a probe".
C4: The capacitance within the scope. (sorry, this should have been "C3".)
If C2 is adjusted so that the value of C2 in parallel with C4 is 9x C1, then we have a properly compensated probe with good high-frequency response. For an intuitive idea about how this probe behaves at high frequency: The load that the signal at the probe tip sees will be 9Mohm in parallel with about 3pF, which gives an approximate RC time constant of ~ 30E-6s == 5.3kHz. So you can see that for the majority of the probe bandwidth the characteristics are determined by the capacitors, not the resistors.
This means that for signal frequencies above 5kHz, the loading effect on that signal is due to the probe capacitance rather than its resistance. At 100MHz, the impedance of a 3pF capacitor is just 530 ohms, and at 500MHz it will be just 106 ohms. Hence the reason why good probes tend to have lower values for C1. If the loading effect of ~500 ohms is excessive for the circuit under observation, then consider using a x100 probe (exchange gain for bandwidth and lower capacitance at the tip), or an active probe (the probe head contains an amplifier to reduce loading effect of the signal, and to improve frequency response).
In regards to test conditions for passive probes: most are specified with a sig-gen having an internal impedance of 50ohm, but it is recommended to read the technical specifications of the particular probe you are using.
For an excellent introduction to scope probes including passive probes, active probes, differential voltage probes, & current probes, may I suggest the following document may be of some value:
https://download.tek.com/document/02_ABCs-of-Probes-Primer.pdf
Here are some other links that may be useful to understand how passive probes trade-off lower gain for higher bandwidth, and practical ideas on implementing passive probes:
Regarding Passive Probes 1:1 and 10:1
Poor man's x100 oscilloscope probe
Why does capacitive loading occur when using passive oscilloscope probes?