As mentioned in previous answers Azure's Notification Hubs only work for mobile devices because behind the scenes it interacts with the various mobile platforms' push notification services such as the Apple Push Notification Service (APNS). It is not sending the notifications directly to the client. Since there are no push notification services for websites you need another technology.
Azure offers Service Bus Queues which would work, but it also offers SignalR which is probably the best solution in your case, and in fact the one I plan to use for a web frontend I am building for my service. SignalR handles all the low level connection details for you, i.e. it takes care of using the optimal protocol for the browser you are running in which is no mean task! It's fast, scalable and surprisingly easy to implement.