Is there a method to select elements negatively proportionate to a categorical distribution? I have a categorical distribution which depicts the probability of bad choices. I want to select elements negatively proportionate to that categorical distribution, i.e., if my categorical distribution is [30%, 50%, 20%], then the second element (50%) will have the least probability to be selected, and I hope the last element (20%) will have the greatest probability to be selected. Is there such a method?

My current solution is to take the negative value of these probabilities and use the softmax function to transform these values into probabilities.
$$
\sigma(\vec{z})_{i}=\frac{e^{-z_{i}}}{\sum_{j=1}^{K} e^{-z_{j}}}
$$
