I've seen 的 used after a verb like this in other sentences. The only thing I could find about 的 after a verb was when it's used with 是.
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喝的 is something for drinking, simply some drinks. 的 is something, some stuff, unnamed stuff, something related to.
Chinese is less bound to type of words comparing to English.
大的嗎？ 用的嗎？ 十號的嗎？ 位元堂的嗎？ 他的嗎？
Interestingly, you can replace a verb with an adjective, a noun, or a pronoun. 的 is just something related to a word.