Learn Hardcore Japanese: haitatu ga okureru kakuritu ha hikui desu. - The probability that the delivery will be late is low.

In Japanese, a relative clause (like “配達が遅れる” – “the delivery will be late”) modifies the noun 確率 (“probability”) directly. You don’t need a particle (such as の) between the clause and the noun. The structure is simply:
(relative clause) + (noun)
This differs from English, which uses “that”:
the probability (that) the delivery will be late
But in Japanese, “that” is omitted and the clause precedes the noun.

Why is the verb 遅れる in its dictionary (plain) form here instead of 遅れます?

When you use a verb to modify a noun in a relative clause, you always use the plain (dictionary) form, regardless of politeness level. The politeness of the entire sentence is handled by the copula です (or だ in casual speech) at the end. So:
配達が遅れる確率は低いです。
If you tried 遅れます確率, it would sound ungrammatical.

What role does the particle が play in 配達が遅れる?

Within the relative clause, が marks the subject of the intransitive verb 遅れる (“to be late”). Here, 配達 (“delivery”) is what becomes late. You generally cannot replace this が with を, because 遅れる is intransitive, and you shouldn’t use は here unless you want a special contrast (which sounds odd in a modifying clause).

Why is は used after 確率 instead of another particle like が or を?

In the main clause, は marks the topic:
“As for the probability that the delivery will be late, (it) is low.”
If you used が there, it would simply mark the subject, but は highlights “確率” as what you’re commenting on. を is never used with adjectives like 低い.

Why do we say 低いです and not 低いになります?

低い is an i-adjective. To make it polite, you add です directly:
低いです.
You do not use ～になります with adjectives. ～になります is for turning nouns/adjectives into polite noun phrases (e.g., 簡単になります is not standard either). Stick with i-adjective + です.

Could we express the same idea with 可能性 instead of 確率? What’s the difference?

Yes, you could say:
配達が遅れる可能性は低いです。
確率 (“probability”) is more quantitative or mathematical, implying a calculable percentage.
可能性 (“possibility”) is more qualitative, like saying “it’s unlikely” in everyday speech.

Can I drop です at the end in casual conversation?

Absolutely. In casual speech, you’d say:
配達が遅れる確率は低い。
Omitting です makes the sentence less formal. In written or polite contexts, keep です.

How would I turn this into a question: “Is the probability low?”

Simply change the intonation (in speech) or add か (in writing/polite speech):
配達が遅れる確率は低いですか？
Or casually:
配達が遅れる確率は低い？
Both mean “Is the probability that the delivery will be late low?”