The mathematical concept of "distance" is quite broad but then again rigorously defined. In general the distance function (or metric) has to have certain properties. The Levenshtein Distance (LD) is a metric for measuring the "amount" of difference between two strings.

In your case the question is different. You don’t compare two strings but a string and a glob. By definition this is not possible unless the glob results in one string only. Otherwise the LD is simply not defined.

In the example you give: you suggest that LD(*cxd*,adcdef)=1. But this is only so when *cxd* expands into one string only which is one edit operation away from adcdef.

Maybe you could generalize the distance function for your particular application. It might not be a proper distance function anymore but may still be useful depending on your particular problem. After expanding the glob into {s1, s2, …, sn} you could determine the LD for all those strings with the original string: {d1, d2, …, dn}. Depending on what meaning it has to you, I don’t know the particular application of it, you can then take the lowest, highest, average or whatever value that makes sense to you.

I wonder what the particular application is you're after.