One way to do that is to have the custom dropdown function return the custom html. Then you can call it inside your add_dropdown_to_posts and put the returned content into a helper variable. After that just prepend the custom html to the $content variable that the the_content filter provides.
Like this,
function my_custom_dropdown_html() {
return '<html stuff here>'; // you could put your html also in a variable and then return that.
}
function add_dropdown_html_before_the_content($content) {
$dropdown = my_custom_dropdown_html();
// if statement just to be safe - e.g you change the custom function output to something else than string of html and forget you've used it here
if ( $dropdown && is_string( $dropdown ) ) {
$content = $dropdown . $content; // prepend custom html to content
}
return $content;
}
add_filter( 'the_content', 'add_dropdown_html_before_the_content' );