Random based on area

I have an array of elements:

$arr = array(
  '0' => 265000, // Area
  '1' => 190000,
  '2' => 30000,
  '3' => 1300
);

I want to get random index based on the area (Array value). I need the area with big value be selected more frequently. How can I do this?

What I have now:

$random_idx = mt_rand(0, count($arr)-1);    
$selected_area = (object)$arr[$random_idx];

Thanks!