Your example sentence for Hobson's Choice is completely wrong, as pointed out by other forum writers. It's like you read your own writing but can't get unstuck from the stereotypical answer that "we all know is true." That type of bad thinking is what leads most people to using the expression in error, as you did. Your sentence was simply about two unappealing choices that a person in jail has to choose from. That's life, sorry about that. A Hobson's Choice is no choice at all, except the alternative not to choose in the first place.