Well, obviously copyright laws vary by country, but what are you planning on doing with it? Downloading it to view and save? Stream? But the letter of most copyright law, it's propbably illegal. Doesn't mean that the police will be knocking down your doors to arrest you if you download the TV show...well, you never know.
Using a P2P file sharing problem is completely legal ... as long as you use it to share files you have the right to own. File sharing programs are just tools. Like any tool, you can use it legally or illegally. I can chop a salad with a knife or I can use it to commit murder.
Legally speaking, P2P file sharing programs still exist because they potentially can be used legally. I can put my open source software up on a P2P network as a way of distribution. I can also put a bootleg movie up on a P2P network.
When it comes to music sharing, a group of kids can put music from their after-school band up on a P2P network as a means of creating an audience and getting their music "out there". In many cases, P2P networks are the only outlets for content creators and artists to find an audience. On the other hand, they can also be used to distribute well-known music without the approval of the record companies, who are losing money when people download their music instead of buying it at the store.
I would also add that if it is an old TV show, it may have been released into the public domain and/or the original copyright holders no longer claim rights to the property. In such a case it would not be illegal for you to download and watch the show from any source.
This is common enough but will depend on the owning company, as some are happy to release their stuff for public consumption when they no longer feel it is potentially profitable, others seem to hang onto it forever in order to maybe sell the rights to produce sequels/remakes/spinoffs etc.