Tim Bowen sheds some light on the origins and definition of the phrase Hobson's choice.
We use this expression when we mean there is no choice whatsoever. For example, in a situation where you want something to drink and you discover that you only have tea, you might say “It’s Hobson’s Choice, I’m afraid. We only have tea”.
The expression is said to derive from the business practices of a 17th century stable-owner called Thomas Hobson. Unlike other stable-owners, Hobson did not give his customers any choice when they hired a horse from him. He always gave them the horse that happened to be nearest the door. Hobson would not change this practice, no matter how important or rich the customer was. If the customer did not want to take the horse nearest the door, he would not get one at all. Now in any situation where there is only one option, we can call it Hobson’s Choice.