Noted! Can most any scope take x10 probes or does the unit have to be engineered as such? E.g., just as it is a bad idea to plug 12V or 18V into a 9V only pedal is there a similar relationship for probes? Thank you!
No damage the probe is only passive.
The basic idea is it is a resistive divider which forms a 1/10 divider. They increase the impedance at the expense of losing the signal. I'd say most professional people use x10 probes and only switch to x1 when they need to look at very small signals.
The circuit is something like the one shown below. Take note of what parts lie in the oscilloscope and what parts are in the probe. Instead of Cp adjustable you will get a fixed Cp and a second variable cap in parallel with cs *inside* the probe connector.

The purpose of the capacitors is to form a 1/10 divider for high frequency to counteract the probe cable capacitance Cc, which you cannot remove. Without the addition of the capacitors the probe would roll-off in the 1kHz to 10kHz. A good probe could do 100MHz.
In order to measure correctly, the probes require calibration. It's simple to do. You only need to recalibrate when you move probes to another oscilloscope because Cs is not fixed or defined to be a specific value.
https://www.electronics-notes.com/articles/test-methods/oscilloscope/scope-probe-compensation.phpA few of things worth remembering:
- You will lose 1/10 the signal. So when you take measurements on the screen you have to multiply the readings by 10.
(Digital oscilloscopes with on screen measurements often have setting which multiplies the numbers for you, some
have special probe which detect the setting.)
- Because you lose signal your oscilloscope is less sensitive. Usually no problem for real oscilloscopes with the exception
of perhaps some old tube based oscilloscopes from the 50's and 60's. Some of the cheap ebay modules have limited
sensitivities which can be an annoyance with x10 probes.
- Real oscilloscopes have a fairly will defined input impedance in terms of resistance and capacitance (it covers a narrow range). That means x10 probes tend to work without thinking about it. If those really cheap ebay probes use 5% tolerance resistors that could introduce an additional 5% reading error with a x10 probe. Most will use 1% but there's always some dodgy stuff to be aware of.