Add a default style if no Featured image is selected

You can test if the $thumb has any contents and then apply a class to the featured image block that you can use to hide the container.

<?php
    $thumb = wp_get_attachment_image_src(
        get_post_thumbnail_id($post->ID),
        'full'
    );
?>

<div id="post" class="featured-image <?php echo empty($thumb) ? 'no-featured-image-class' : ''; ?>" style="background-image: url('<?php echo $thumb['0']; ?>')">