This is the 5147th most frequent Turkish word.
ihtimalinin
"Of its possibility" or "of the possibility."
Here, "ihtimalinin" refers to the "probability of failing" and is the genitive construction relating to the verb "başarısız olma" (failing).
Bu sınavda başarısız olma ihtimalinin düşük olduğunu düşünüyorum.
I think the probability of failing this exam is low.
In this sentence, "ihtimalinin" is associated with "yağmur yağma" (raining), indicating the genitive possession of this event's probability.
Yağmur yağma ihtimalinin çok yüksek olduğu söyleniyor.
It is said that the probability of rain is very high.
Here, "ihtimalinin" is utilized to construct the genitive form linking to "seyahatin ertelenme" (the trip being postponed).