For your wild example it is impossible to do taint analysis. Taint analysis can work only if you know bitcoin address involved in transaction ( or previous few immediate transactions ) is considered bad like say some exchange got hacked and coin moved to one particular address ( address x ). Now if your bought coins has origin from that coins, you may consider it tainted. But you must know the address x is tainted.

Some tools you want to know :

https://blockchain.info/taint/1dice6GV5Rz2iaifPvX7RMjfhaNPC8SXH

Chianlysis.com is one company working on it. There are few more startups working in this direction.

But again, even if you know coins are clean you should not accept it from anonymous identity. If you really want to make sure you are not involved in such transactions, prefer reputed exchanges and companies.

On a side note, if your bank account gets transfer from some shady account you should worry exactly same way. Do you expect transfer in your bank account from anonymous person without identifying him ? Bitcoin is same. You have to use same precautions with bitcoin too. I do understand your question is more about tools and technical information, but trust me there is no way one can make sure bitcoins he has received are not so called tainted ( except you mine and get fresh block, which also may be in some countries/jurisdiction illegal if thet think mining or bitcoin is illegal ) I have always insisted people to understand that bitcoin is not only example of cutting edge technology, its cutting edge example for law and its interpretation too.

Regards