You want to prevent Slicer 2 and Slicer 3 from filtering out options in Slicer 1. Instead, you want Slicer 1 to always display both "program" and "non-program" options. To do this:

Go to "Edit Interactions", click on any of your visuals (e.g., your slicers). You'll see an "Edit Interactions" option under the "Format" tab in the ribbon.

Select Slicer 2 and Slicer 3 one by one, and ensure that they do not cross-filter Slicer 1. You can do this by selecting the "None" interaction for Slicer 1 when editing slicer interactions. You can add further to it by making a flag type measure to indicate whether a value should be greyed out in slicer 1 and then add it as a conditional formatting for the slicer one. It will grey out the option which is not applicable or has been filtered out in a particular situation.