Togakure said:
It's not a simple ratio from what I've been able to tell. Other lords are eligible, they have renown, and may or may not have fiefs. I believe both are taken into account. I've noticed that if I have a fief and there are lords without fiefs, I've never been offered a second fief until the fief-less lords have gotten one. If we have equal fiefs, sometimes I get it and sometimes not--but I've noticed that if my renown is a lot higher than theirs, I get it more often. The king's favor seems to play a part when both of these factors are close.
You can see this illustrated (in .96, at least) if you back a claimant, convince some lords to join your cause, and then take a few new castles or towns: the claimant will generally ask you who should get the newly available fiefs, and your relationships with your fellow lords (and your claimant) will change, depending on your answers. From observation:
-- your relationship with the lord you grant the fief to increases.
-- your relationship with lords with no or less fiefs than those of the awardee decreases.
-- your relationship with a lord's enemies decreases.
-- if you always grab the fiefs for yourself, your relationship with everyone else decreases.
Mind you, this was also somewhat random, since quitting and restoring the game yielded different results. However, I found that the safest bet was to keep track of who got the last fief and make sure not to give fiefs to the same lord twice in a row.
Perhaps the same principles hold for Kings.