Learn Farsi: احتمال دارد شدت باران تغییر کند. - It is probable that the intensity of the rain changes.

ehtemâl dârad is an impersonal expression meaning it is probable or there is a probability. Because it describes a general situation rather than the action of a specific person or thing, the verb dârad always stays in the third-person singular, no matter what happens in the second half of the sentence.

I know that probability phrases trigger the subjunctive mood, but why doesn't the verb taghyir konad have the subjunctive be- prefix?

The verb here is the compound verb taghyir kardan (to change). When forming the subjunctive of a compound verb, Farsi speakers usually drop the be- prefix. So instead of taghyir bekonad, it simply becomes taghyir konad, with the subjunctive mood still doing its job to show uncertainty.

Is it possible to insert a connecting word between the probability phrase and the rest of the sentence?

Yes, you can insert the word keh (that) right after ehtemâl dârad, but it is completely optional. In Farsi, the connecting keh is very often dropped to make the sentence flow faster, as seen here.

How are the words sheddat (intensity) and bârân (rain) linked together grammatically?

They are linked using the ezâfe, which is an unwritten -e sound added to the end of the first word. It is pronounced sheddat-e bârân. This acts like the English word of to show that the intensity belongs to the rain.