They do, but the problem is, it's the same bloody thing. The question you have to ask yourself is where the burden of proof lies. In court, the general rule in most civil law countries (and I imagine common law countries too) is that he who claims something, must prove it. Here the original claim is that there is a God, thus the believers would have to prove it. Furthermore believers are generally talking about one specific God, while non-believers don't believe in God as a concept. This means that the believer only has to prove one thing, while the non-believer would have to prove loads. For this reason also, it makes much more sense that the believer has to provide the proof.