The result of some built-in string function length(s), that, depending on the implementation of the string type, either returns the header integer stating the size, or counts the length until the terminator symbol and returns that integer.
That doesn't sound like something you'd need to do statistics on. Once you learn something about the string length, you basically just know it.
Improper priors are not useful on their own: the point of using them is that you will get a proper distribution after you update on some evidence. In your case, after you update on some evidence, you'll just have a point distribution, so it doesn't matter what your prior is.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
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