If we just treat anything happening no matter how likely or unlikely equally then much of this forum is just utterly useless. Discussions would just boil down to 'Oh, and wouldn't it be cool if the French installed a monkey as king of Siam?' 'Yeah! Then like...It could conquer China!' 'Woo! Then maybe the monkey China empire can colonise Russia!'
The point of AH is to discuss realistic alternatives. Not just any old random thing we can think of.
The US did have no chance of winning the Trent War short of major ASBs like the Royal Navy all deciding to defect to the US or some sort of weird steel eating bacteria to infect Britain.
On the first bolded area: There is a difference between say 5-3% and .000000001%. The latter I am fine with people saying it will never happen. The Former, I am not fine with.
Now, a blockade is normally something that really hurts your Economy. However, it doesn't cripple it. Look at the CSA, Imperial Germany, and other scores of nations. People say that the US wouldn't be able to fight a war without Gunpowder (due to the British possessing the single major source for a critical ingredient of it). Well, as far as I know the CSA did just fine, and they also had to deal with a blockade.
On the senond bolded part: You may call them ASB's, I call them luck. Don't say that Britain's Military can't act stupid after the Battle of New Orleans, where Andrew Jackson took 4,000 Militia and gave a highly experienced and highly trained British force of 8,000+
an absolute thrashing. The lesson is that sides with superiority tend to act with arrogance and stupidity, and in many cases, this is their downfall, to forces they on paper should crush. Have this happen enough (for Britain that is), and you can very well have the US and Britain come to a White Peace and have the US then conquer the CSA.
Basically, to understand my way of thinking, play rock-paper-scissors with a friend. Make a game where you have a go at it 6 times. If you win once, you win overall. If you never beat him once, he wins overall. The majority of the time, you will win. However, every once in a while, he will win.
That is my thinking of the liklihood of Britain winning in the Trent War.