All numbers have precision. 0 is 0 ± 0.0000001 or something. The thing after ± is itself never zero. In the case of 0, the precision in relative terms is always [∞]%. The number is perfectly dominated by its uncertainty.
This is probably why the vacuum isn't empty. 0 particles != 0 particles.*
If the possibility of measurement exists at all, there is something there to be measured. You can only have 0 if numbers don't make sense at all in that context - if the question itself is wrong.
*P.S. When you think true things, the world has a tendency to make sense. When you think false things, it is hard to think of an example.