Ordinary coax can't be generally used to extend scope probe cables, because scope probe cable is special with high resistance inner conductor to force it to use RC-mode propagation instead of LC propagation. Using RC mode dampens the unterminated reflections so they are not a problem.
It might be better to use "Z0 probe"-like construction (suitable series resistance right at the point of the measurement, ordinary 50 ohm coax and 50 ohm termination at the scope end) than try to extend the cable of an existing probe.
But if the signal integrity is not a problem, you might still try if that extension works for you or not.
Regards,
Janne
Interesting... I've tried my theory with a 1.5m 50 Ohm coax and a TEK P2200 probe, TDS2014B.
1x termination looks OK, rise and fall times are OK.
If you use 10x termiantion, it becomes a mess. No other setting was changed.
The probe shielding is around 0 Ohm (DC) while the inner part, without the tip is ~300 Ohm.
I might have been half wrong, in this case I would bring the measured signals outside and use the scope as is.
I guess I've learned something today.