The Problem
$my_posts doesn’t contain any posts. It contains post IDs and likes. And you’re dropping both into post__in, which can’t work. I guess even the number of posts wouldn’t work if the plugin(?) wouldn’t add any post with a 0-x integer to the db-table per default.
The Debug
Try the following:
$my_likes = $wpdb->get_col("SELECT like_pid FROM wp_likes_count ORDER BY like_count DESC");
echo '<pre>';
print_r( $my_likes );
echo '</pre>';
which will likely show you an array containing two sub-arrays.
Way to a solution
Then try to get the sub-array you need and drop it into your query. Example: 'post__in' => $my_likes['like_pid'].
The Plugin
Anyway, a plugin should store something like this in the post_meta table in a field and not add an unnecassary table for something like that. There should be a facebook plugin by otto in the wp.org repo. This one’s much stronger, better written & by a trustable author. You should consider switching.