Is the result of analogRead(A3) always zero, or is the outcome of your calculation in post #1 already zero regardless of the reading of A3? It's not clear from your post.
Did you in fact look at this? You didn't respond, but it's a relevant remark.
This is not a schematic of your setup. I know this because (1) you state above you use A3, and (2) there's no Arduino in the picture and no power supply for it; long story short: a COMPLETE schematic, please.
One more thing: in theory there's nothing wrong with having an Arduino directly measure the voltage over a shunt resistor. But personally I think it's kind of tricky to directly connect an Arduino to what is apparently a piece of high-power electronics without any apparent interfacing or protection.
Alright, actually one more thing still: you mention a "resolution" (wrong term!) of 75mV for 50A. But what is the actual range that you need to measure, and at what resolution? I.e. the 4.88mV step size of the Arduino, corresponding to a 3.3A step size as @chrisknightley pointed out, is that sufficient? It's a very low resolution measurement you're performing.
Frankly, this all sounds very haphazard to me. Hence the emphasis on providing a good and complete schematic so that the people here can give you some advice on how to go about this effectively and safely.