From Rgb to Cmyk

Dyalog APL, 16 15 bytes

1-⊢(÷,255÷⍨⊢)⌈/

1 minus 1-
 X divided by ÷ Y, followed by , 255 dividing 255÷⍨ Y ⊢, where
  X is itself ⊢ (i.e. the list of RGB values), and
  Y is the max /⌈ (of the RGB values).

$$ \begin{cases} J = max(R,G,B)\\ C = 1-\frac{R}{J}\\ M = 1-\frac{G}{J}\\ Y = 1-\frac{B}{J}\\ K = 1-\frac{J}{255}\\ \end{cases} $$

TryAPL!

Credits:
 ∘ -1 byte by ngn.

C#, 88 86 85 84 bytes

(r,g,b)=>{float[]a={r,g,b,1};var j=a.Max();a[3]=j*j/255;return a.Select(x=>1-x/j);};

output for 108,174,106:

0.3793104
0
0.3908046
0.3176471

Since OP allows function I submitted only the lambda. You can find a running demo on .NetFiddle. I am not a golfer, I post for fun. Also, it is my first answer \o/. Feel free to comment any improvement :)

Kudos to Leaky Nun for the formula.

caveat: it doesn´t work for [0,0,0] (thank you Titus)

Python, 46 bytes

lambda*c:[1-i/max(c)for i in c]+[1-max(c)/255]

Requires input to be floats in Python 2, fairly sure it doesn't in 3.