Values in a specified category need only show up when a specified value>zero?

I am creating a spreadsheet that allocates hours to different categories of work - for example, "Fire Protection". I need the allocated hours for all of the different Fire Protection duties to only show up when a value greater than zero is entered in the column at the top of this category entitled "Fire Protection". If "Fire Protection" has a value of zero, then all fire protection-related duties will automatically be zero as well - in effect, this category of hours is nullified.

I hope that is a clear explanation, because I have no idea how to accomplish this!