You will have to pay $1.08 to send a message to a stranger
Facebook introduces paid messaging to users that are not on your friends list or your friends’ friends list.
At first this option will be introduced in the UK in test mode and charge $1.08 per message.
Paid message will be delivered to the user’s inbox marked as "important". Also Facebook reserves the right to send free messages, but they will be delivered to "Other" destination folder.
Facebook notes that the service is not available to persons under 18.