Olmert's ability to (a) become powerful very, very quickly and (b) get the party to somehow officially designate him as its leader very, very quickly. Odds that either of those things will happen are difficult to determine - for instance, nobody knows how or where Kadima would hold primaries (or who would vote in them). There are a lot of really talented politicians who have risked their political careers on Kadima, and they probably can't go back to their old parties (Peretz was already stacking Labor with his union friends before Kadima existed, while everyone knows [Netanyahu] to be vindictive and petty). So there are a lot of really big brains with an incentive to make Kadima work.

. . . Olmert has three months to prove that he's able to lead the country. But he has to act quickly to demonstrate that he's even going to be running as a leader of anything.

A caption contest from happier days.

UPDATES: Meyrav Wurmser in National Review thinks Kadima was an anomaly created by Sharon's outsized influence on Israeli politics, which is better off without it.

Also Joel Rosenberg on Bibi's chances:

All but written off by many political observers in Israel who thought he would be trounced in a three-way battle with Sharon, the former Prime Minister could be Israel's next Prime Minister. He won the recent Likud primaries decisively. He has taken a tough position on Iran. And he has a track-record of controlling Palestinian terrorism while also negotiating peace deals (he gave Hebron to Yasser Arafat, though the Israeli Left never gave him much credit and the Right was furious). But Netanyahu's success is by no means certain. His party is badly divided. The Israeli press hates him. And he would need to find a way to win over centrists while not causing the Right to abandon him. It won't be easy. But suddenly, it's possible.

Boker Tov, Boulder contrasts some Israeli and Palestinian reactions to Sharon's illness, but Palestinian reactions - at least at the official level - are more complex:

U.S. National Security Council official Elliott Abrams and State Department official David Welch were to have met with Sharon on Thursday evening, apparently to urge Israel to reverse a decision to ban Palestinian voting in disputed Jerusalem. . . . Abbas has said he may not hold elections if Jerusalem, chttp://www.keshertalk.com/cgi-bin/mt.cgi?__mode=view&ping_errors=1&_type=entry&id=5457&blog_id=1&saved_changes=1laimed by the Palestinians as a capital, is excluded. “We hope that this (Sharon’s illness) will not affect what we had expected of the Israelis,” said Palestinian negotiator Saeb Erekat. If Olmert puts off a decision on Jerusalem, “it means the Palestinian election is going down,” Erekat said.

. . . . Arab TV broadcasters beamed out largely straightforward, nonstop live coverage about Sharon.
Ahmed Jibril, a radical Palestinian leader in Damascus, Syria, called the stroke a gift from God.
. . . . But a Palestinian commentator on the Saudi-owned Al-Arabiya network offered Sharon unexpected praise as “the first Israeli leader who stopped claiming Israel had a right to all of the Palestinians’ land,” a reference to Israel’s Gaza withdrawal. “A live Sharon is better for the Palestinians now, despite all the crimes he has committed against us,” said Ghazi al-Saadi.

The nutcase running Iran sees Sharon's illness as another opportunity to posture. (via Meryl, doing her own update)

Comment from Winds of Change:

IMO this means that Israel won't attack Iran. All politics is local. The Israelis will have to settle their differences over Sharon's replacement before a successor will be strong enough to do anything risky aboard. Even if means being nuked in the meantime.

So it's up to us.