How can I add virtual column to collection?

I have a output structure of $collection like this:

I have array with sample data:

$arr = [
    'id_1' => 10,
    'id_2' => 30,
    'id_3' => 20
]

I need add $arr to above collection and then i have it’s output:

After that, i can filter with price:

$collection->addAttributeToFilter('price', ['gt' => 12]);

How do I achieve this?