For example, X is a random integer from 1 to 16. Now I get a piece of information: X is 3, 5, 9, or 14. This has 2 bits of information for the knowledge about X. But if the list of options is random enough, I'd have to list all four integers to describe this knowledge, which is much more than 2 bits. It may need more information, if the probability distribution is not uniform, and I attach a probability to each of the options.

Is there a term for this phenomenon?