Calculated field BG color change automatically

If you use simplified notation for division, you will get an error when field A is empty.
Instead, try something like this as custom calculation script of field "C":

var a = Number(this.getField("A").valueAsString);
var b = Number(this.getField("B").valueAsString);

if(!isNaN(a) && !isNaN(b) && a !== 0)
event.value = b/a;
else
event.value = "";

if((!isNaN(a) && !isNaN(b)) && (a !== 0 && b !== 0)){
if(b>a)
event.target.fillColor = color.green;
else if(b<a)
event.target.fillColor = color.red;}
else
event.target.fillColor = color.transparent;