There is one way to do it, but it's bad: eval()

echo (isset($html) && !empty($html)) ? eval($html) : show_404();

I would personally ob this from a file, buffering it and then use get_ob_clean to get the result, like so:

    ob_start();
        include 'temp_file_with_html_in';
        $view = ob_get_contents();
    ob_end_clean();

Note:

• Your English is unclear so I am not sure exactly what you want
• This may not work exactly as you want

Maybe a better explanation of what $html is and how it is sourced would help?

The quickest way I can think of (though a better solution could likely be found if I knew how $html was created) is to plop the contents into a tmp file and then include it. This is really a warning flag that there are architectural problems with the program, however (for instance, why can't the php interpolation be done when $html is created?)

$tmpFile = tempnam('/tmp', 'my_app_namespace');
file_put_contents($tmpFile, $html);
include $tmpFile;
unlink($tmpFile); // cleanup

edit, from Drupal 7

As you hinted in the comment, Drupal 7 does indeed contain what I would call a trick: prepending a PHP closing tag to the code you pass to eval, which will then handle it like a regular php include:

From Drupal 7's ./modules/php/php.module, around line 79, adapted a bit:

ob_start();
print eval('?>' . $html);
$output = ob_get_clean();