First of all give a name to your select. Then do:
<select name="my_select">
<option value="1" <?= ($_POST['my_select'] == "1")? "selected":"";?>>Yes</options>
<option value="2" <?= ($_POST['my_select'] == "2")? "selected":"";?>>No</options>
<option value="3" <?= ($_POST['my_select'] == "3")? "selected":"";?>>Fine</options>
</select>
What that does is check if what was selected is the same for each and when its found echo "selected".