How do I add to the list table a filter?

You can use views_edit-post hook to do so. It is a possible variation of views_{$this->screen->id} and resides in class-wp-list-table.php.

add_filter('views_edit-post', 'my_post_views' );
function my_post_views( $views ){
    $views['html_class_name_for_li'] = 'the html'; // ex: <a href="#">something (11)</a>
    return $views;
}