Why a != b != c is not equal to a != b and a != c and b != c?

I want to check if 3 values a, b , c are not equal to each other. Given that a == b == c equals to a == b and b == c and a == c, why does python give a different answer for a != b != c ?

Thanks!

This is a task from an introductory course to Python:

"How many of the three integers a, b, c are equal?"

This is a simple task and I got the correct answer with the following:

a = int(input()); b = int(input()); c = int(input());

if a != b and a != c and b != c:
    print(0)
elif a == b == c:
    print(3)
else:
    print(2)

Yet, I can not understand why a != b != c wouldn't do the job in the initial if statement.

From a != b != c I expect the same as from a != b and a != c and b != c

Copyright Notice：Content Author:「Jironymo」，Reproduced under the CC 4.0 BY-SA copyright license with a link to the original source and this disclaimer.
Link to original article：https://stackoverflow.com/questions/58395948/why-a-b-c-is-not-equal-to-a-b-and-a-c-and-b-c