Answer: 117

Method:

Given the constraints in the description of the puzzle,
there are 12 possible combinations of the padlocks:

009
018
027
036
045
117
126
135
144
225
234
333

Call the last digit N after Nick's initial.

Notice that if N=3, 8 or 9, then Nick would see that there was
just one combination possible, but because Nick did not solve the puzzle
within a few minutes then Carol (and we) would conclude that:

3 < N < 8

That leaves:

027
036
045
117
126
135
144
225
234

When Carol considered this list she immediately knew the combination.

Given that Carol already knew the middle digit, only one combination
in the list is unique: 117. For any other possible middle digit, there
are 2 or 3 alternatives. We conclude that Carol's digit is 1 and therefore
the combination is 117.

We don't need the clue of being told that Belle's digit is 1.