We conduct a survey on a large representative sample of Slovak population to examine the role of analytic thinking, scientific reasoning, conspiracy mentality, and conspiracy beliefs in trust in COVID‐19 fake news and willingness to share it. We find that the ability to distinguish between fake and real news about COVID‐19 is significantly negatively correlated with conspiracy mentality and with beliefs in pandemic‐related conspiracy theories. Analytic thinking is not a significant predictor. Although fake news is generally less likely to be trusted and shared than real news, when fake news is consistent with preexisting opinions, people are more willing to share it compared with belief‐consistent real news. We also find that people are mostly overconfident in their ability to distinguish between fake and real news, and we identify a subpopulation of people that refuse to get vaccinated who trust fake COVID‐19 news significantly more than real news. Thus, consistency with one's beliefs is the best indicator of trust in fake news and willingness to share such news.