Did most Jedi Knights eventually become Jedi Masters or did only a small fraction attain that rank?
This is covered in the The Jedi Path : A Manual for Students of the Force.
The rank of Jedi Master is the highest formal recognition one can achieve in the Jedi Order. It is not a requirement, nor does it mark the end of your journey. Jedi who have attained this rank are the fewest in membership, and are outnumbered by even the younglings.
Although this book is no longer considered canon (after the April Purge), it was written from an in-universe perspective by respected Star Wars author Daniel Wallace and with the assistance of LucasFilm's own people.
According to the Jedi Master article on Wookieepedia:
The rank of Master was a title bestowed upon very few Knights in every generation. As such, Masters made up the smallest percent of the Order's membership.
Unfortunately, it would be difficult to make a more informed comparison without having access to actual census data from the Jedi Order. Based on the various depictions in media, however, it would seem that Jedi Knights far outnumber Jedi Masters by at least 10 to 1.