Peg Game explanation

A lot of people had a lot of question while solving Peg Game problem @ Qualification Round of Facebook Hacker Cup. Here is my understanding of this puzzle. I hope I'm right and my solution will be accepted.

Imagine a game board and try to get "boundary condition"...

where:

• blue arrows shows "far left" and "far right" cases;
• red arrows shows situation that will never happend (probability 0).
  

Also imagine "missing of a peg" situation,
where:

• blue arrows shows that ball goes forward to the bottom with the same probability as it has before.
  

Test case from problem description


1st test case from example input