The complement of an event occurring is that it does not occur.
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"one third" is not an event and so cannot have complement nor a probability.
With the information that is available from the question, it is impossible.
The probability of no rain is the complement of the probability of rain. If the probability of rain is 0.99, then the probability of no rain is calculated as 1 - 0.99, which equals 0.01. Therefore, there is a 1% chance of no rain.
The complement involves probability. Say the probability of choosing a red marble was 3/10. So the complement, or the chance of not choosing a red marble is 7/10. Think of it as the opposite of the probabilty. You simply subtract the numerator from the denominator and you have the complement. (10-3=7 in this case, then you would put your difference over the probabilities denominator, so it would be 7/10.)
Read the introduction to probability and probability measures at StatLect.com