node.js + express: `sendfile` to Ajax request giving a 404

Node noob here. :) I'm making an Ajax request with the code

var path = "/path/to/file.html";

$.get(path, function(data) {
    $("#post").html(data);
});

and on the server side, responding with

app.use(express.directory(__dirname + '/public'));

app.get('/path/*', function(req, res) {
    var is_ajax_request = req.xhr;
    if(is_ajax_request)
        res.sendfile(req.path);
    else
        res.sendfile('public/index.html');
});

where the actual file is located at public/path/to/file.html. For some reason Ajax is giving me the error

GET http://localhost:3000/path/to/file.html 404 (Not Found)

even though the path is correct for sure. In fact, if I remove the whole app.get function it finds the file no problem. Is there another way I should respond to the Ajax requests?