In light of the failure of attempts to analyse knowledge as a species of justified belief, a number of epistemologists have suggested that we should instead understand justification in terms of knowledge. This paper focuses on accounts of justification as a kind of ‘would-be’ knowledge. According to such accounts a belief is justified just in case any failure to know is due to uncooperative external circumstances. I argue against two recent accounts of this sort due to Alexander Bird and Martin Smith. A further aim is to defend a more traditional conception, according to which justification is a matter of sufficiently high evidential likelihood. In particular, I suggest that this conception of justification offers a plausible account of lottery cases: cases in which one believes a true proposition – for example that one's lottery ticket will lose – on the basis of probabilistic evidence.