var newOptions = {"value1": "displaytext1",
 "value2": "displaytext2",
 "value3": "displaytext3"
};

var $el = $("#selectbox");

$el.empty(); // remove old options

$.each(newOptions, function(value,displaytxt) {
$el.append($(" ").attr("value", value).text(displaytxt));
});

$el.empty() will remove all the option. To removing all the options but the first, you can use the :gt selector to get all the option elements with index greater than zero and remove them

$('#selectbox option:gt(0)').remove();

instead of $el.empty();