Assuming your data at A1 looks like this:
0 0 1 2 3 4
0 0 1 2 3
0 0 1 2
1 0 1
then this Conditional Format will highlight
only the first zero in the third row:
Enter this Conditional Format at B1 and
Copy Paste Special Format to all:
=ISNUMBER(B1)*(B1=0)*(SUM($A1:A1)=0)*(COUNTA($A1:A 1)=0)