When performing a Kolmogorov-Smirnov test, we compute the KS distance between the empirical cumulative distribution function, and the theoretical one. Then, we compare this measure with the corresponding critical value, and reject the null hypothesis (the sample is drawn from the reference distribution) if the distance is larger than the critical value.
But if we look at the table of critical values, we can see that they increase as $\alpha$ gets smaller. My understanding was that $\alpha$ was the risk of making an error, so I would expect that the higher $\alpha$ is, the higher the risk, and so the higher the critical value should be.
Why does the critical value increase when $\alpha$ decreases?