Can Nassau County Probation charge a probationer for area in the home beyond the control of the probationer if this is stipulated in his conditions?

If its inside the same residence... its assumed they have control or access.

If its inside the same residence... its assumed they have control or access.even if the entire house is a rental and everyone has access to all parts of the house except for the actual room rented by the probationer

It only matters that the person on probation has access to everything in the house because they live in that house. Entering another room in a house you reside in is far different that entering a room in the house next door where you don't.

You could not have two people on probation renting separate rooms inside the same house.

THey can make the assumption about that gun and that marajuana because they have access. Plausible denyability doesn't apply to people on probation.