A type I error is the probability of rejecting the null hypothesis when it is true, which is the alpha level of the test.

A type II error is the probability of not rejecting the null hypothesis when we should reject it, which is Beta.

By intuition, the greater the departure from Ho, the less likely that departure will be detected, therefore there is a less chance of rejecting the null hypothesis, which decreases the chance of Type II error, which means Beta is smaller