You are right to examine the evidence closely. (There are others here who don't firmly believe the evidence at all, but merely stoke the coals in the hope that there will eventuate a mud-slinging contest.)
Can you explain how you ascertained the probability of Bibisara being not guilty to be less than 10%?
Sure, if you believe the `toilet' evidence, then you believe she is guilty. However, this evidence is not strong -- there are serious questions pertaining to its reliability.
1. The testimony is hearsay. Who knows what Miss Solozhenkina actually alleged to her father initially, if anything. I suspect he has just made the whole thing up and told his daughter later to go along with it.
2. Miss Solozhenkina is not the most reliable witness, given she is a weaker rival who would benefit from any finding against Miss Assaubayeva.
3. Whatever happened in the toilet, the evidence is severely weakened by the failure of Miss Solozhenkina to raise it with any authority at the time, and also by the fact that no other witnesses have come forward to confirm the allegations. They will find it very difficult now to prove that any wrongdoing was committed. (However, the Solozhenkins are well aware that it is also impossible, after the fact, for Bibisara to disprove the allegations and overturn the presumption of guilt -- so they will continue to attest to her guilt in the hope that others will join in.)
Normally people don't rape, kill or commit armed robbery either. Even though your statement is true, I'm not sure that it would be ruled as admissible.
If the chess examples are irrelevant, then is there something more to the prosecution case that we are all missing out on?