There may be more than 1 transition matrix which works.  For a distribution
of (0.4, 0.3, 0.3), there are at least these two:

|  0,   0.5,  0.5  |
|  .67, 0,    .33  |
|  .67, .33,  0    |


|  0,   .25,  .75  |
|  1,   0,    0    |
|  .33, .67,  0    |


I found a way to find them all given rational probabilities, but it's SLOW!
Also, I still don't know when it will and won't work without trying all
possibilities.

I'll try to clean it up,

Chris