Monty Hall: switch or stay?

Read these three steps first if this is your first time

1. There are three buttons, and only one is correct. You choose one first.
2. The host knows the answer and opens a different button that must be wrong.
3. With two buttons left, you can switch or stay with your original choice.

The key is that the host is not opening a random button. A wrong option is removed on purpose, which means the information has changed.