How to understand structure of sentences in probability

Here in my textbook, it says

And I am supposed to pick the correct order of size for the probabilities above.

The book says the probabilities are

Then my question is for example in (II), why is it not that $P(\mathrm{II})=\Pr(\text{Breakfast} \mid\text{ Senior})$?

Because I feel like if you wrote (III) as a conditional probability, you should write (II) as a conditional probability too.

What am I missing here?

For case I, you are selecting from someone who surely is a senior.

For case II, The person that you select randomly is from the pool of teenager, of which he might be a junior. It is not given that the person is a senior.

For case III, you are selecting from someone who eats breakfast. It is given that the person eats breakfast for sure.

I think you are asking how the English grammar of each description implies the corresponding probability. This is non-trivial in general, which is why it is better to express things in unambiguous notation than in English.

It will be clearer if you parse each sentence into the grammatical subject (bold) and predicate.

(I) A randomly selected high school senior eats breakfast

(II) A randomly selected teenager is a high school senior who eats breakfast

(III) A randomly selected teenager who eats breakfast is a high school senior

The subject (especially when described as "randomly selected", as here) is often understood as describing the event (subspace) being conditioned on, and then the predicate describes the event being evaluated within the conditioning. A key difference between (II) and (III) is that the "who" clause is in the predicate in (II) but in the subject in (III).

As noted, English can be ambiguous. For example, "eats breakfast" might mean eats breakfast every day, or most days, or one particular day. And "teenager" seems to be an implicit universe here, with an assumption being made that all high school seniors are teenagers.

As another example, "the probability that a salesperson knocks on my door" has an unclear meaning because of the physical context involved. The relevant universe/conditioning might be clarified by a phrase such as "given that one day passes" or "given that a salesperson knocks on someone's door" or "given that someone knocks on my door".

I'm not 100% sure this is entirely correct, but maybe it helps. Consider this dataset:

For (I) you start from the subset of students that are senior (A, C, D) and among these students look for those who eat breakfast (A). So:

𝑃(𝐼)=𝑃(𝐵𝑟𝑒𝑎𝑘𝑓𝑎𝑠𝑡|𝑆𝑒𝑛𝑖𝑜𝑟) = 1/3

For (II) you are looking at all students (5) and you ask who is senior and eats breakfast. So:

𝑃(𝐼𝐼)=𝑃(𝑏𝑟𝑒𝑎𝑘𝑓𝑎𝑠𝑡∩𝑆𝑒𝑛𝑖𝑜𝑟) = 1/5

(III) is similar to I but this time you start with the subset that eats breakfast (A and B) and you look for those who are also senior:

𝑃(𝐼𝐼𝐼)=𝑃(𝑆𝑒𝑛𝑖𝑜𝑟|𝐵𝑟𝑒𝑎𝑘𝑓𝑎𝑠𝑡) = 1/2