How does humidity vary with height in the Earth's atmosphere?
Humidity strongly varies as a function of time and space, which is why standard atmospheres like CIRA may choose to omit it at all.  It simply doesn't make sense to include an “average” humidity profile, because such an average is not meaningful.

However, there are other sources for relative humidity profiles.  You can obtain them from reanalysis data.  If you want probabilities, you could calculate them from reanalysis.  I have not used probabilities, but I have used profiles from Anderson et al. (1986) in the past:

Anderson, G. P., S. A. Clough, F. X. Kneizys, J. H. Chetwynd, and E. P. Shettle (1986), AFGL atmospheric constituent profiles (0–120 km), AFGL, TR-86-0110.

Anderson transcribes them in his paper, which is in PDF and not ideal to read.  The same data are distributed along with the Atmospheric Radiative Transfer Simulator (see also Wikipedia article).  This radiative transfer model comes with a set of XML files, that includes profiles from both CIRA and from Anderson et al.  Those are not probabilities but “typical” H₂O profiles for five scenarios: tropical, mid-latitude summer, mid-latitude winter, sub-arctic summer, and sub-arctic winter.  For example, a mid-latitude summer H₂O profile can be found at this link.  The data are in XML so should be easy to read, but they also provide reading routines for Matlab and Python.  The unit is volume mixing ratio, which may actually be more suitable than relative humidity if you are interested in calculating air density.