Facebook Fan Page – Question

If you are running a competition through your page, you will have the post regarding the competition on your page. The easiest way would be to post a "Congratulations" message with the profile picture of the winner. Many pages run contests through their page. Real fans who have 'Like'd your page will see it in their wall.

Contests/competitions/sweepstakes/etc

must not use Facebook features or functionality as a promotion’s registration or entry mechanism. For example, the act of liking a Page or checking in to a Place cannot automatically register or enter a promotion participant

and

must not condition registration or entry upon the user taking any action using any Facebook features or functionality other than liking a Page, checking in to a Place, or connecting to your app. For example, you must not condition registration or entry upon the user liking a Wall post, or commenting or uploading a photo on a Wall

and

must not use Facebook features or functionality, such as the Like button, as a voting mechanism for a promotion

See Facebook's Promotion Guidlines for the rest of rules and regulations.