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I've read that no article is used before cardinals (one, two, three... etc) but ordinals, but here in the following sentence this rule is voided. What is the reason behind it?
The cities show an absence of automobiles (which is "neither backwardness nor delay, but a rejection," to quote Robert Guillian), advertising, neon signs, and the three fevers of money, alcohol, and sex.
When using a cardinal number to form a noun phrase you can always use the definite article to identify a specific instance of a number of things, in the same way as you would with any other noun phrase.
Usually, you shouldn't use an indefinite article when using cardinal numbers with objects because the objects are usually plural, and the indefinite article is not used with plural nouns. If the number is one, this is used to replace the indefinite article as they are synonyms in this context. The exception to this is when a number is used in a compound adjective, describing the make-up of the object. Here the object can still be singular, and the number is used to describe the adjective, not to count the object.
There was one monster. - No need for "a" because "one" replaces it.
There was a one-eyed monster. - Now we need an "a" because "one" is used in the compound adjective "one-eyed" - it describes the number of eyes, not the number of monsters.
There were many monsters. / There were five monsters. - No need for an "a" because "monsters" is plural in both cases.
The five monsters terrified the town. - You are identifying a specific instance of "five monsters", so you can use "the".
In your extract, the is used because it is referring to three specific fevers (which are then listed), not just any three fevers.
The definite article "the" may be used when referring to a set or group of things:
The three musketeers.
The four horsemen of the apocalypse.
The seven deadly sins.
The ten commandments.
and so on, this usage is typical.
The indefinite article "a" is also often used, but the cardinal number is usually hyphenated:
A one-time code pad.
A four-handed card game.
A thirty-seater bus.
