Steps to reproduce:

1. Create a host with trigger in it. Add trigger to map as map trigger element.
2. Move trigger into problem state.
3. Disable host.

Result:
Few observations:

1. In map trigger's label still indicates that trigger is in problem state.
2. In map element's context menu 'Problems' item is inactive.
3. Problem also is not visible in Monitoring -> Problems view.
4. If same host added in map, it also shows no problems.

Expected:
I assume that trigger should be disabled. Observations 2-4 might be correct.