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The solution for your requirement is demonstrated in the attached workbook.
To understand how it works please first consider the basic logic I applied. I wanted a formula which counts cells which meet certain criteria. Using the same COUNIF() function you can count cells containing values >, <, =, <= or >= zero. This function is developed and demonstrated in column H of the Solution worksheet.
The demonstration shows when the count equals zero. This is where you can see if the condition for the count has been adjusted correctly. Modify the data and watch the effect on column H or modify the function to demonstrate a different result, but ignore the CF at this point.
The conditional formatting formula is developed from the function in column H. It isn't identical. The formula used for the CF evaluates the result. "If the function returns 0, then apply the format": =(COUNTIF($B3:$F3,"<=0")=0). You can see the function from column H embedded in the CF formula. So, by embedding a different function in the CF formula you can modify its effect on the colouring. Observe that the range is defined differently in column H and in the CF formula. That is because column H has a purpose slightly different from that in the CF. It isn't a copy-paste job. Rather, it is a logic developed in column H and then applied in the CF formula.
The final task is to apply the CF formula correctly. It is designed (by means of the range definition) to be applicable to all cells in a range (the Applies To range you can access from the CF Manager dialog box). If you make alterations to the range by other available means Excel will tend to create a new rule each time, using the same formula but processing it separately. That will slow down your worksheet and may, when carried to the extreme, crash it.