// get the cats this product is in
$terms = wp_get_post_terms($post->ID, 'product_cat');


$cats = array();
$total = array();
// if there is only one category jump out.
if (count($terms) == 1) {
    $cats = $terms[0]->term_id;
}else{
    // remove anything that is a parent cat
    foreach ($terms as $k => $term) {
        if ($term->parent === 0) {
            unset($terms[$k]);
        } else {
            // build list of terms we do want (children)
            $cats[] = $term->term_id;
        }
    }
}
foreach ($terms as $k => $term) {
     $total[] = $term->count;
}
// wp_reset_postdata();


$related_products = new WP_Query(
    array(
        'posts_per_page' => 3
        'order' => 'DESC',
        'orderby' => 'rand',
        'post_type' => 'product',
        'post__not_in' => $post->ID,
        'tax_query' => array(
            array(
                'taxonomy' => 'product_cat',
                'terms' => $cats,
            )
        ),
    )
);

echo "<pre>";
            var_dump($cats);
        echo "</pre>";

        echo 'Total products with these terms: '.array_sum($total);

        echo "<pre>";
            $total = $related_products->post_count;
            echo 'Total in query: ';
            var_dump($total);

            // var_dump($related_products);
        echo "</pre>";