What does the bandwidth of a probe mean?
It means pretty much the same as any other bandwidth: It tells you where the response of the circuit is down 3dB. In practice, if you're looking at signals with frequencies more than about 1/10 of the bandwidth, you can expect significant distortion because of the loss of the higher frequencies.

The tricky thing here is that the circuit in question has three parts: lumped resistance and capacitance in the probe; distributed resistance, capacitance, and inductance in the cable; and lumped resistance and capacitance in the oscilloscope's input circuit. So you can't look just at the input resistance and capacitance of the probe; that's only part of the overall circuit. That's useful information to figure out how the probe loads the circuit being measured, but it's not all there is to calculating the input bandwidth.