2 ways you can do this
1. Change from a prompt selector to 3 drop downs and use 3 queries to display the content for these drop downs. The first query contains only country, the second has a filter on the selected country and returns only customer and the third has a filter on country and customer and returns only product. All queries refresh on change of prompt value.
2. Use one query and 3 drop downs. The drop downs has filtered values as a selection which will include all values that is equal to the selected value.
Option 1 is the better, but if you don't have too much data option 2 can work and it will be quicker.
Cheers,
Josh