For a 93.75% confidence interval, draw 5 points (iid). If the last four are all greater than the first one, your CI is the whole real number line, otherwise it’s the empty set.
Once you draw some actual data and get a specific interval, you want to ask about some degree of belief that your specific interval contains the actual parameter. In the case that your CI is all numbers, you know for a fact that it contains the true parameter value. In the case that your CI is the empty set, you know for a fact that it doesn’t contain the true parameter value.
I like this CI procedure because it demonstrates two things. 1) The kind of reasoning for going forward from an unknown parameter to a random interval is very different than what you have working backwards from a specific interval back to the parameter. That asymmetry can be WEIRD. 2) The weirdness is possible if you limit yourself to only the CI definition, meaning that if you want it to be useful, you need something that rules out weird shit like my example.
The properties of specific CI procedures people actually use are generally much much better than what is allowed by the definition of a CI. If you want useful reasoning backwards from the interval, don’t try to reason solely from the definition of a CI.