PHP checkbox validation, if else issue

I have a checkbox in my HTML file:

<input type="checkbox" id="kopia" name="kopia" class="form-input" value="0">

I'm trying to pass to the PHP file (via AJAX) a couple of values, one of them is a boolean value created by a checkbox (simplified):

name: "kopia"
value: document.getElementById("kopia").checked

If I check via console, it returns true if checked and false if unchecked.

document.getElementById("kopia").checked

If I check via PHP file, it behaves the same:

echo $_POST['kopia']

But when I write something like this:

$checkbox = $_POST['kopia'];
if ($checkbox){
    echo "hey";
} else {echo "bye";}

It always returns "hey", no matter if the checkbox was checked or not. I don't get it. Even if I make something like this:

$checkbox = $_POST['kopia'];
if ($checkbox){
    echo $checkbox;
} else {echo "bye";}

It never returns "bye", no matter if the box was checked or not, but returns true if checked and false if unchecked. This thing has already stolen a couple of hours and that's a couple of hours too much. Any idea, hint?