What is the probability of making a Type II error if the null hypothesis is actually true?

zero. We have a sample from which a statistic is calculated and will challenge our held belief or "status quo" or null hypothesis. Now you present a case where the null hypothesis is true, so the only possible error we could make is to reject the null hypothesis- a type I error.

Hypothesis testing generally sets a criteria for the test statistic to reject Ho or fail to reject Ho, so both type 1 and 2 errors are possible.