Learn English – why is “advice” used as an uncountable noun and “suggestion” used as a countable noun

People is usually the plural form of person:

One person, two people, three people, ...

What you'll notice here is:

• People is countable.
• People is plural, even though there's no -s suffix.
• The singular form is always one person, never *one people.
• The indefinite forms include a person and people.

Here are a few more details you can safely ignore:

This is called suppletion, and it's much like how we say went as the past form of go, even though went was originally a different word (the past form of wend).

The plural persons exists too, but it's limited to a few formal legal contexts. In everyday life, people use people as the plural form and ignore the word persons entirely.

And now, here are some details you shouldn't ignore:

People isn't just used as the plural of person. It's also used as a separate word meaning "the persons living in a country and sharing the same nationality" (Collins). And when it's used in this sense, both the singular and plural forms look different:

One people, two peoples, three peoples, ...

Although these are grammatical, we're not terribly likely to count peoples this way. This term is more likely to be used in phrases like the French people, the Navajo people, or the Native American peoples (note the plural, as there is more than one group of Native Americans).

You can tell the difference by how the word looks. If it's two people, it's the plural of person. If it's two peoples, it's referring to two groups of people, each of which has a distinct identity. And if it's one people, it must be referring to a group.

But most of the time, people is the plural of person.

Intelligence is not being used as a countable noun in Clever Hans. There's some information ellipted; read the sentence like this:

... animals had an amount or degree of intelligence equal to that of humans.

Here, intelligence is qualifiable but not quantifiable.

However, it is possible to use intelligence as a countable noun, though this usage is less common. See definition 1.1 here and definition 2 here. A common usage of this involves a countable but heterogeneous group of either intelligent minds or types of mental processing. For example:

• There are many different types of intelligence. (Here intelligence means efficacious manner of thinking.)
• Space exploration might discover intelligences other than our own. (Here intelligence means conscious mind or being.)