Consider the following experiment: randomly place the balls in the way you mention, choose one of the red balls randomly, and tag it as "first". From the point of view of the first ball, the other two red balls are placed randomly.
Denote by $x,y,z$ the intervals between the red balls, starting with the first and going clockwise. So $x+y+z = 97$, and $x,y,z \geq 0$ are integers. All possible triples $x,y,z$ satisfying these conditions are equiprobable. It is now possible to obtain exactly the entire distribution by enumeration of the $\binom{99}{2}$ cases.
Here is the entire distribution (multiplied by $\binom{99}{2} = 4851$): $ \begin{array}{ccccccccccc} 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 \\ 291 & 282 & 273 & 264 & 255 & 246 & 237 & 228 & 219 & 210 & 201 \\ \\ 12 & 13 & 14 & 15 & 16 & 17 & 18 & 19 & 20 & 21 & 22 \\ 192 & 183 & 174 & 165 & 156 & 147 & 138 & 129 & 120 & 111 & 102 \\ \\ 23 & 24 & 25 & 26 & 27 & 28 & 29 & 30 & 31 & 32 & 33 \\ 93 & 84 & 75 & 66 & 57 & 48 & 39 & 30 & 21 & 12 & 3 \end{array} $ The interested reader can easily prove the formula $h(x) = 300 - 9x.$