There are countless such markets throughout both history and the contemporary world. Consider your local red light district. In most jurisdictions prostitution is illegal in some way or the other; yet nonetheless there are countless places where people go to buy and sell sex work. Similarly, in many parts of the world it is easy to find pirated music or films (etc.) for sale in certain places, the trade in restricted animal and animal parts is flourishing in China at various medicine shops and restaurants despite various laws there forbidding much of that trade, etc.

If you think that this isn't secretive enough to really be a black market, then the issue is instead that you shouldn't expect a market to be a true secret. Markets can't work unless the buyers and sellers expect to be able to trade, and these expectations crucially require knowing how to be able to trade. Insofar as this means that knowing how to buy/sell the illicit goods means knowing where to go to buy or sell them, this means there are black markets you go to in order to do so.

There are many reasons such black markets can exist even if their existence is both widely known and illegal. One reason may be that it would be pointless for law enforcement to shut them down, since they can disappear and re-apprear easily and move easier than you can shut them down. Or trying to shut them down can be counterproductive, in that the resources you need to even attempt it would make law enforcement less effective overall (this is why limited prostitution and drug trade is permitted in the Netherlands--Dutch vice law on the books is relatively conservative, but they have a legal principle that they only try and enforce laws they believe can be enforced productively, and the legal system has decided that many vice laws would be counterproductive to enforce). Or de facto enough of the people responsible for law enforcement may turn a blind eye for all kinds of reasons, ranging from taking a cut through to genuinely believing that the black market does more good than harm.