In most cases I think the probability would go up, but it depends on what other information you have, especially information about the stability of the PM's government and how transitions of power take place in that country.
The main reason for the probability to go up is that the announcement provides evidence that the PM has a weak hold on power. If he's announcing now that he'll be resigning soon, then there's a decent chance that the opposition is capable of driving him out of office at any time.
However, it's possible that you already knew how weak a hold the PM had on his job. And it may also be the case that transitions of power tend to happen in an orderly way in this country, and that the PM's announcement initiates the orderly procedure. So now that an election has been announced, they're very likely follow through and hold the election as planned. In that case, you might adjust the probability downward.
Suppose you want to assign a probability that a government will fall (ie the Prime Minister resigns) before the end of the year. Lacking any particular information - I haven't even told you which government it is - you say "Obviously, it's 50% - either it happens or not" (or perhaps "Oh, say, 10%, governments can usually rely on lasting a year at least"), put that prediction into your registry, and go on with your life. Then, on December 1st, you hear that the Prime Minister in question has promised to resign and call an election in March of next year. How should this affect your probability that he will resign before the end of this year?
I see several arguments:
1. Having gotten this public commitment out of him, his opponents have no particular reason to push his government further. It should become more stable for the finite time it has left. My probability of a resignation in December should go down.
2. His opponents were able to extract such a promise; it follows that he cannot be quite confident in his ability to survive a vote of no confidence. Such a signal of weakness might easily lead to a "blood-in-the-water" effect whereby his opponents become more aggressive and go for the immediate kill. His government will surely fall before this attempted compromise date; my probability should go up.
3. The March date wasn't chosen at random. Presumably there is something the PM thinks he can get accomplished if he retains his position until March, but not if he resigns right away. So, presumably, his opponents will be all the more eager for him to resign before he gets it done, whatever it is; they will put more resources into toppling him. Again, my probability should go up.
The question is not hypothetical: I was faced with precisely this problem in December, and got it wrong. I'd like to see how others think about it.