In order to solve this problem I had to break down what I was trying to do. I was attempting to remap various values (floats in each colour channel) to another value between 0 and 1.
In other words I was trying to find the percentage distance of that colour point to the maximum or end point. This may seem abstract, but it's fun to think of these colours as graphs or vectors.
Here is an image to explain. Someone posted it on the unity forum.
A helpful commenter on that thread suggested that if the point was 35% along the line then one could use linear interpolation to find its position. Unity has a function to do this.
For my problem however, I knew the position but I did not know the percentage. Or rather, the GPU knew the position (as it was the input and the percentage was the output).
It was then that I remembered that Unity also has an inverse linear interpolation function - which was exactly what I needed. After a little bit of research I found the formula for this:
f(x) = (x - min) / (max - min)
In the shader I used the above formula to calculate my output.
Below is an image demonstrating the effect.