Cutting K Trees out of N

There is a field with $N$ trees, and each one gets $R$ meters taller every year. However, at the end of every year, exactly $K$ of the trees--randomly selected--get cut down to their stump (but they don't die).

At the end of a year after an infinite amount of time passes, what will be the average height of all the trees?

For example, with $N = 3, K = 1,$ and $R = 1,$ the following is a possible scenario:

• Year 0: Tree heights $= [0,0,0]$
• Year 1: Tree heights $= [1,0,1]$ $\Big($ #2 was cut, and the average height is $\frac23\Big)$
• Year 2: Tree heights $= [2,1,0]$ $\Big($ #3 was cut, and the average height is $\frac33\Big)$
• Year 3: Tree heights $= [3,2,0]$ $\Big($ #3 was cut, and the average height is $\frac53\Big)$
• Year 4: Tree heights $= [4,0,1]$ $\Big($ #2 was cut, and the average height is $\frac53\Big)$
• Year 5: Tree heights $= [0,1,2]$ $\Big($ #1 was cut, and the average height is $\frac33\Big)$
• Year 6: Tree heights $= [1,2,0]$ $\Big($ #3 was cut, and the average height is $\frac33\Big)$
• Year 7: Tree heights $= [0,3,1]$ $\Big($ #1 was cut, and the average height is $\frac43\Big)$
• $\quad \vdots$