How do I update a field of a meta box?

Okay. I solved the problem myself. I was not populating the the array of a meta_key the correct way.

Below, you will find a working solution:

$check_post_exists = function( $title ) use ( $wpdb, $postTypeArray ) {

        // Get an array of all posts within our custom post type
        $posts = $wpdb->get_col( "SELECT post_title FROM {$wpdb->posts} WHERE post_type="{$postTypeArray["custom-post-type"]}" AND post_status="publish"" );

        // Check if the passed title exists in array
        return in_array( $title, $posts );
    };

    $i = 0;
    $e = 0;

    foreach ( $posts() as $post ) {

        // If the post exists, skip this post and go to the next one
        if ( $check_post_exists( $post["properties/ID"] ) ) {
            $e++;
            continue;
        }

        $i++;

        // Insert the post into the database
        $post["id"] = wp_insert_post( array(
            "post_title" => $post["properties/ID"],
            "post_type" => $postTypeArray["custom-post-type"],
            "post_punktcat" => array( 4 ),
            "post_status" => "publish"
        ));

        // Set post category to 4
        wp_set_post_terms($post["id"], 4, 'punktcat', false ); 

        $meta = get_post_meta( $post["id"], 'fredningszone_data', true );

        $fredningszone_data = array(
            "id" => $post["properties/ID"],
            "navn" => $post["properties/NAVN"], 
            "kontaktsted" => $post["properties/Kontaktsted"],
            "fredningsperiode" => $post["properties/FREDNINGSP"],
            "periode_type" => $post["properties/PeriodeType"], 
            "lovgivningsgrundlag" => $post["properties/LOVGRUNDLA"],
            "bemaerkning" => $post["properties/BEMARKNING"],
            "www" => $post["properties/WWW"],
            "www2" => $post["properties/WWW2"],
            "geometry" => $post["geometry/type"]
        );

        // Update meta box values
        update_post_meta($post["id"], 'fredningszone_data', $fredningszone_data);
        //update_post_meta($post["id"], 'fredningszone_data', $post["zoneid"]);
        update_post_meta($post["id"], '_location', $post["zoneid"]);
    }