As I understand it, you're trying to show the fundamental connection between the first state and the second. The second state caused the first, so it should follow that its present when the first is. You're not looking for the "opposite", (an imprecise term usually meaning inverse) you want the converse. Using that understanding, we could have:
Its raining. Naturally, its cloudy.
Where its refers to the local weather condition by context, and the lack of change in context implies that the two are related, so naturally implies that there's a fundamental relation. You could also use:
Its raining. Of course it's cloudy.
Hinting that raining should inherently imply cloudy.
Its raining. Its obviously also cloudy.
Explicitly saying that there's a known relation there.
Alternatively to all of that, you could join the two sentences, resulting in the smoother:
Its raining, so naturally its cloudy.