Here is a blog entry, or tutorial if you will, that achieves something very similar.
Their setup slightly different, but this is the summary:
use ffmpeg to convert your input into mpeg1video:
ffmpeg -i rtsp://whatever -f mpeg1video -b 800k -r 30 http://localhost:8082/yourpassword/640/480/
Install node.js with stream-server.js script from jsmpeg and ws ws WebSocket package.
To view the stream, use the stream-example.html and jsmpg.js from the jsmpeg. Change the WebSocket URL in stream-example.html to localhost and open it in your favorite browser.
Update an SO topic suggest two other working solutions, with <video> tag: with stream-m Java server or with ffserver.