"Though these numbers aren't actual, he characterizes the system like this: the first time you kill a monster, you have a 16% chance of getting the item. The second 32%, third 48%, and this progresses to 100%. But he warns "it also got rid of all of the good streaks and we had to raise the base drop percentage higher." 
-Christian Nutt gamasutra article.
Why in this day and age are there still completely random drops to begin with?
By design this makes the player feel like he's not making any progress by grinding.

Let the op know after each kill with a bar or a number that his chances of obtaining the said item is approaching 100%

Another way to do it is just to give a lot higher chances of drops but split the loot into parts like in monster hunter.
You need 4 Lagisaurus horns to craft one weapon. One drops almost every time the party focuses their attacks on it and players grind the same fight but with a sense of purpose.

This random crap is an MMO relic to keep people in an imaginary treadmill that's likely not going anywhere. You can make us grind just us much by actually making us feel like we're approaching our goals by being more honest in game design.

Rolling the dice after successfully overcoming a challenge is just undermining all the skill the player just showcased by killing the mob. This is 2011. Act accordingly!