Nobody in practice actually uses information entropy as described by the description or by what the kata asks us to calculate.

What information entropy are usually used for is:

Given this data/password generation scheme, how many bits of information do they contain?

What is being calculated instead is:

Given this string of characters, if I randomly pick one character from the string, how many bits of randomness do I get?

(You can easily verify this by checking what x actually means: it's not each character, it's each possible state. Therefore all possible states being calculated in the kata is all the possible indices of the string, aka you're picking a random character from the string.)

So the entire description is misleading at best at the moment.

I run into a timeout with 123456790, while all other tests are passed.
Any suggestions?