Zvabolis

I figured it out using a combination of the two code snippets.

This is the original piece of code:

<?php if ( '' != get_the_post_thumbnail() && ! post_password_required()  &&  ! get_theme_mod('hide_singlethumb') ) : ?>
		<div class="entry-thumbnail">
			<a href="<?php the_permalink(); ?>" title="<?php echo esc_attr( sprintf( __( 'Permalink to %s', 'zuki' ), the_title_attribute( 'echo=0' ) ) ); ?>"><?php the_post_thumbnail(); ?></a>
		</div>

The amended code is as follows:

<?php if ( '' != get_the_post_thumbnail() && ! post_password_required()  &&  ! get_theme_mod('hide_singlethumb') ) : ?>
		<div class="entry-thumbnail">
			<a href="<?php the_permalink(); ?>" title="<?php echo esc_attr( sprintf( __( 'Permalink to %s', 'zuki' ), the_title_attribute( 'echo=0' ) ) ); ?>"><?php the_post_thumbnail(); ?></a><?php $get_description = get_post(get_post_thumbnail_id())->post_excerpt;
  if(!empty($get_description)){//If description is not empty show the div
  echo '<span class="caption_arrow"></span><br><div class="featured_caption">' . $get_description . '</div>';
  } ?>
		</div>

I added everything except the_post_thumbnail(); from my second snippet of code right after the </a> of the original code.