In order to remove a specific All() and Pubished() post counts from Posts-editor page you can:
// Create a specific hook
add_filter("views_edit-post", 'custom_editor_counts', 10, 1);
function custom_editor_counts($views) {
// var_dump($views) to check other array elements that you can hide.
unset($views['all']);
unset($views['publish']);
return $views;
}
Lets go more advanced and remove All() from Posts-editor admin table and Published() from Pages-editor admin table.
// Create a hook per specific Admin Editor Table-view inside loop
foreach( array( 'edit-post', 'edit-page') as $hook )
add_filter( "views_$hook" , 'custom_editor_counts', 10, 1);
function custom_editor_counts($views) {
// Get current admin page view from global variable
global $current_screen;
// Remove count-tab per specific screen viewed.
switch ($current_screen->id) {
case 'edit-post':
unset($views['all']);
break;
case 'edit-page':
unset($views['publish']);
break;
}
return $views;
}
Refferences:
[Hide the post count behind Post Views (Remove All, Published and Trashed) in Custom Post Type]
UPDATE
Updated an answer with a code how to update posts count for specific user, excluding "all" and "publish" views. Recently tested on WP 4.3 twentyfifteen.
add_filter("views_edit-post", 'custom_editor_counts', 10, 1);
function custom_editor_counts($views) {
$iCurrentUserID = get_current_user_id();
if ($iCurrentUserID !== 0) {
global $wpdb;
foreach ($views as $index => $view) {
if (in_array($index, array('all', 'publish')))
continue;
$viewValue = $wpdb->get_var("SELECT COUNT(*) FROM $wpdb->posts WHERE post_type='post' AND post_author=$iCurrentUserID AND post_status='$index'");
$views[$index] = preg_replace('/\(.+\)/U', '(' . $viewValue . ')', $views[$index]);
}
unset($views['all']);
unset($views['publish']);
}
return $views;
}