Your CMM vendor should be able to supply you with the K1 and K2 values applied to their statement of total CMM measurement uncertainty. The K1 value is a constant (non-length dependent) uncertainty, composed of probe reproducibility, system resolution, and short period scale errors, among other things.
Assuming that your true position tolerance is quite small, for the purposes of your situation, you can disregard the K2 value, which involves long-period scale errors, system squareness, etc.
Therefore, the K1 value represents the measurement uncertainty in any one measurement before you begin to move the CMM axes. Although it is not a one-for-one conversion, this K1 value should be a pretty good yardstick to determine your confidence level for your true position measurement.
Good luck!