An antiprediction is a statement of confidence in an event that sounds startling, but actually isn't far from a maxentropy prior. For example, if someone thinks that our state of knowledge implies strong ignorance about the speed of some process X on a logarithmic scale from nanoseconds to centuries, they may make the startling-sounding statement that X is very unlikely to take 'one to three years'.
Often, it is sufficient to see the privileged possibility as but one among many equivalently probable events, and use maximum entropy principle to divide probability equally among them, leaving each very little. For example, each of the millions of possible lottery combinations are equally likely, and so any one person's ticket is very unlikely to come up: winning the lottery should be seen as one possibility among millions, not one of the two possibilities of "winning" and "not winning".
Privileging the hypothesis is our term for what happens when somebody clings to a small area of the possibility-space despite the lack of any evidence distinguishing in favor of that possibility versus many, many other equally likely alternatives.