Convert RGB to RGBA over white

Question

I have a hex color, e.g. #F4F8FB (or rgb(244, 248, 251)) that I want converted into an as-transparent-as-possible rgba color (when displayed over white). Make sense? I'm looking for an algorithm, or at least idea of an algorithm for how to do so.

For Example:

rgb( 128, 128, 255 ) --> rgba(   0,   0, 255,  .5 ) rgb( 152, 177, 202 ) --> rgba(  50, 100, 150,  .5 ) // can be better(lower alpha) 

Ideas?

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FYI solution based on Guffa's answer:

function RGBtoRGBA(r, g, b){     if((g == null) && (typeof r === 'string')){         var hex = r.replace(/^\s*#|\s*$/g, '');         if(hex.length === 3){             hex = hex.replace(/(.)/g, '$1$1');         }         r = parseInt(hex.substr(0, 2), 16);         g = parseInt(hex.substr(2, 2), 16);         b = parseInt(hex.substr(4, 2), 16);     }      var min, a = (255 - (min = Math.min(r, g, b))) / 255;      return {         r    : r = 0|(r - min) / a,         g    : g = 0|(g - min) / a,         b    : b = 0|(b - min) / a,         a    : a = (0|1000*a)/1000,         rgba : 'rgba(' + r + ', ' + g + ', ' + b + ', ' + a + ')'     }; }  RGBtoRGBA(204, 153, 102) == RGBtoRGBA('#CC9966') == RGBtoRGBA('C96') ==      {        r    : 170,        g    : 85 ,        b    : 0  ,        a    : 0.6,        rgba : 'rgba(170, 85, 0, 0.6)'      } 

Answer 1

Take the lowest color component, and convert that to an alpha value. Then scale the color components by subtracting the lowest, and dividing by the alpha value.

Example:

152 converts to an alpha value of (255 - 152) / 255 ~ 0.404  152 scales using (152 - 152) / 0.404 = 0 177 scales using (177 - 152) / 0.404 ~ 62 202 scales using (202 - 152) / 0.404 ~ 123 

So, rgb(152, 177, 202) displays as rgba(0, 62, 123, .404).

I have verified in Photoshop that the colors actually match perfectly.