Open your file into Photoshop, open the channels panel, you will notice that the black and white areas are presented in all RGB channels.
Edit > Convent Profile.
In the convert to profile dialogue box go to the section
Destination spaceand dropdown the list to
A warning dialogue will appear just click OK .
In the custom CMYK dialogue box in the separation options section select the Black Generation to
Maximum, you will notice that the colored curves disappeared and we preserve the black curve only in the gray ramp chart.
Click OK for applying the black and change the profile custom name to your own and press OK to applying our custom color profile.
Now open the channels panel, you should see the black and white background are dropped in the black channel only.