Jon W on "Showing only the last 3 comments for a post / page"

For my mobile theme I wish to show only the last 3 comments for that post (or page) and the new comment form.

I added this code to the comments.php

<?php $args = array(
    'number' => 3,
    'post_id' => $post->ID,
    'status' => 'approve'
);
$latest_comment = get_comments( $args );
if( $latest_comment ) foreach( $latest_comment as $comment ) { ?>
<?php echo $comment->comment_author; ?>: <?php echo wp_html_excerpt( $comment->comment_content, 500 ); ?>..."<br /><br />
<?php } ?>
</p>
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<?php comment_form(array('comment_notes_after' => '')); ?>

However, this shows the last 3 comments for the whole site, not for that page. Better than showing all comments (some pages have hundreds) but not what I wanted to do.

Does anybody know how to get the current page comments to show?

Many thanks

Jon.