It means the market doesn't think it's likely but it doesn't mean it's 75%. To illustrate why that makes no sense, if Musk had offered $35 instead of $54, the buyout would be much less likely, since the price would be way lower and the board and shareholders less likely to accept it, yet under your model the likelihood would go up.

Estimating probability from price action is something you can do, but not like you did it.

Why would the likelihood go up under his model? If Musk had only offered $35 and people thought that was only 20% likely to happen (for the reasons you listed) then the market price would have only gone up to $31.

Say I offer to buy Apple for a penny/share. The price for their shares won’t move because of my offer but may move from normal market conditions. If the shares increased a dollar the day after my offer, would you say there’s a greater than 100% chance of my offer being accepted?

There of course the implicit assumption here that Musk's offer is causally related to Twitter's stock price. OPs comment make sense if you keep that in mind.

Interesting. As a point of comparison, when Microsoft bid a 62% premium for Yahoo back in '08, Yahoo stock spiked about 48%. Doing the math, the market placed the likelihood at 48÷62=77%.

In other words, the market is wildly optimistic.

If it is a general trend on takeover optimism, we should play that angle and become millionaires

Where does the $30 come from? The last time Twitter was that low was May 2020. There’s no evidence that the market values Twitter at $30 without Musk’s bid.

That fair value valuation is subjective. The $35 number was arbitrarily chosen and is unknown, so the derived probability is meaningless as well. The possibility of a take over changes the potential long term valuation of a company and thereby changes the demand for the stock. Basically, if enough people think the buyout would happen, or would just make Twitter more valuable (as a stock) than it is now, that increases the number of buyers and hence drives the price of the stock up.

If a buyout is certain, then the demand for free money is 100%, and demand for a sure loser is 0% of potential buyers. Hence the share price would quickly converge to a buyout price in that situation.