A way to look at this sentence in another way is:
"Interestingly, nearly/almost two times out of three, the glass broke when it hit the floor."
Meaning, the glass broke one time out of three but not two times out of three, because the second time, the glass cracked, but didm't break. That's why they used the word 'nearly' or 'almost' in this example.
So, interestingly, one time out of three, the events predicted by the experts proved to be wrong, but almost two times out of three.
I hope this helps.