You just are missing the point of colour managment. Don't worry you're not alone, but it is big and important.
Adobe doesn't have a fixed translation. It depends absolutely and completely on the RGB and CMYK profile you use. So when you quote that conversion you're just saying "with my Photoshop settings of [this] RGB profile and [that] CMYK profile I see this conversion". If you don't like the conversion, it usually means you are using the wrong profile for that purpose. A CMYK profile is there to get the best and most accurate conversion of colour for the device you intend to use it on.
It's entirely possible to have a CMYK profile that converts entirely to CMY and has 0% K for all values. You just need to find or make one, and use it.
"Test Screen name" is right about ICC profiles. I'll try explain a bit more.
I see 44431f is a HEX colour. Did you want to make that hex colour into CMYK to print it? Or its just an example?
So you're seeing those CMYK numbers in the color picker I guess?
To illustrate what's happening, when converting from, say, RGB to CMYK, Photoshop (and other Adobe app's) uses 2 x ICC profiles, one of those is the document (image) profile, the other is the selected CMYK profile.
Starting with hex it's a little different (see "Hex" below), but both the RGB and CMYK profiles are still important.
If you were simply using either the color picker to get those CMYK numbers - or for those using image/mode/CMYK then Photoshop will use the CMYK ICC profile selected in the Color Settings dialog as the "destination profile".
This profile is used in a conversion from RGB to CMYK.
When making conversions, I advise clients to take more control and use edit/convert to profile in Photoshop, because it allows for selecting the right CMYK profile for the relevant print process and, also, choice between rendering intents, which do make a difference to the conversion.
But what's most important here when looking for a rich black, is how the ICC CMYK profile was made. At the time of creating an ICC CMYK profile there are quite a few expert options such as TAC (max ink) and Max K (how much black is allowed) also UCR or GCR, for a rich black profile a suitable setting would be GCR and a high black number. Some profile building applications also allow control of a graphically illustrated black generation curve.
Let's do a test, in Photoshop make a new RGB image [file/new], say sRGB. It doesn't matter what size, select all and using the colorpicker fill it with the hex color 44431f, a kind of Army green.
At this time, the hex colour is converted to RGB.
So, beware, your choice of RGB colorspace for the image is important here. I am seeing quite a difference between the hex color 44431f in a new "Adobe RGB" image and 44431f in a new "sRGB" image/document - why? - Adobe is using the RGB document profile in the process of converting the hex to RGB. [the Lab numbers change too, as you'd expect].
Let's leave aside the part where hex gets converted to RGB and move on to the CMYK part of your question.
So, we decided on sRGB for the new image.
The RGB numbers are 101,75,3.
In Photoshop's Color Settings, my rendering intent is Relative Colorimetric with "use black point compensation" checked.
My CMYK option is "Coated FOGRA39 (ISO 12647-2-2004)", with this setting, the info pallet gives the CMYK as 43, 55, 100, 51 when the eyedropper is placed over the image colour.
In Color Settings, if I change my CMYK profile to "ISOcoated v2 (ECI)" [I download that profile from eci.org] the CMYK numbers change to 20, 43, 97, 64.
What's interesting here is that both "ISOcoated v2 (ECI).icc" and Coated "FOGRA39 (ISO 12647-2-2004).icc" are profiles which were were created from the same printed target data (that dataset is called FOGRA 39L), so why the difference in the resulting CMYK numbers above?
Well, Adobe created the "Coated FOGRA39 (ISO 12647-2-2004).icc" profile and they use a different ICC profile creation software to that used by the ECI (Heidelberg PrintOpen). maybe different settings too. You'll see the ECI profile generally uses a bit more black (that's called higher *GCR).
So you can see that even for the same CMYK output device (characterised here in the FOGRA 39Ldata) the numbers making up THE SAME printed colour can differ.
On a well behaved press both those two sets of CMYK values would print the same.
To further illustrate the difference between ICC profiles, lets try starting out with RGB 0,0,0,
"Coated FOGRA39 (ISO 12647-2-2004).icc" gives 86,85,79,100
"ISOcoated v2 (ECI).icc" gives 88,79,65,93
*What is GCR? It stands for Grey Component Replacement.
An RGB file has no "black" channel, black here is simply the lack of red green and blue.
It is possible to just print on paper with just CMY inks, but because of ink density and impurity of colour that's unlikely to give a good neutral or enough density on paper and black would be poor, hence the invention of black in printing as the "key". using black this way saves ink too.
When RGB is converted to CMYK using ICC profiles, GCR takes the "grey component" [the base density] of a colour and uses black to replace the 3 inks which could (in a perfect world) have been used to print that density . So GCR replaces neutral density in both neutral and coloured areas of an image when converting RGB to CMYK.
It is possible to create a CMYK profile with zero K, so just CMY. When using we'd see RGB files converted to just CMY, no K. it wouldn't give pleasing print though, and a lot of ink would be used.
I hope this helps
if so, please do mark my reply as "helpful" and if you're OK now, as "correct answer" so others who have similar issues can see the solution
neil barstow, colourmanagement.net