Based on having the IP-address , how can I find back the corresponding website ? How can I find out that there is a website connected to that IP-address ?
Paste it into a browser window? You can get more info on an IP by going to http://whois.domaintools.com/ip.number.here
You can do a reverse dns. That will only get you a definate answer for a dedicated or vps server. For shared hosting you may find a few hundred sites share the same IP. If you are wanting to report abuse or a problem, finding out the nameservers for shared hosting will usually allow you to contact the correct host.