OK, here is something to try.
Get a 9V battery and use your multimeter to measure the voltage across the battery.
Make a table with 2 columns, Ohms and Voltage. In the first row place 0 in the ohms column (because you didn't have a resistor) and whatever your measured voltage was.
Now get a resistor between 100 ohm and 1k and place it in series with the battery and the multimeter (let''s say you use 220 ohms) Note in your table the resistor value and the measured voltage. The voltage is the same, right?
Now repeat this again with a resistor between 1k and 10k, and again with one between 10k and 100k. You might start to see a small and practically incosequential change.
Now do it again with resistances between 100k and 1M, and then with a resistance between 1M and 10M.
What do you see now?
If your first reading was 9.601 volts and your meter was perfect, the readings would always be the same 9.601 volts.
However your meter is not perfect and forms (in conjunction with the series resistor) what is effectively a potential divider. This means that the meter only sees part of the voltage.
This series resistance works exactly the same way as the impedance of a signal source. There may be a significant voltage present, but you cannot measure it because the impedance of your measuring equipment is too low.
This is often the case with noise that is picked up by some stray wire. It will only affect high impedance devices because the signal itself has a high impedance. A low impedance device will only see a very small fraction.
Go back to the table you drew above and add a third column. In the third column place the difference between the voltage measure in that row and the voltage measured with no resistor.
This swaps things around. If you had a source of 9V with the impedance of your meter, the third column indicates how much of that you would see across a load represented by the resistor.
As you can see, for low to moderate resistance values the voltage is very, very tiny. But it increases dramatically as the resistance rises.
If that 9V were now a noise source generating peaks of 9V, that third column would indicate the height that these noise spikes could reach on your oscilloscope.
If you're following along, you might ask "How does this relate to the oscilloscope probe problem, because there was no resistance there -- it was open circuit?"
The answer is that the signal is AC and there are stray capacitances and inductances which effectively close the circuit and induce the current. Impedance is more than just resistance -- the example above used DC where impedance = resistance.
If you're interested, you can attach various resistors across between the probe and its ground connection and see how the noise varies. You could also do the same with various capacitances and inductances, but don't try to make too much sense out of what happens with them as this is actually very complex.
edit: you'll never understand it 100%, but you'll get closer and closer to that.
