In that case your conclusion shouldn't be that civilizations are only biological. Your conclusion should be: because we have not observed life outside Earth, the more likely thing is that there is not life outside Earth, not that it's biologic.

But I think that you are using correctly your likelihoods but forgetting your priors. The prior in this case is: there is no reason that we know for this not to happen, so, it has to be happening somewhere.