What is the probability it will be a sunny day a year from today?

There's no way to answer this with a single probability. All that can be done is to review weather reports from one year ago, two years ago, three years ago (and so on) and base an estimate (of having a sunny day) on this historical data.

Assuming that your choices are sunny and not sunny. There would be a 50% chance that a year from today will be sunny.

Therefore the answer would be 1/2 or 50%.