Pedantic aside: the word "fortuitous" means "happened completely by chance", which is the opposite of what you seem to be implying here. You probably want a word like "incredible" or "unlikely" instead.
> Many object to the use of fortuitous to mean simply “fortunate” and insist that it should be limited to its original sense of “accidental.” In modern standard use, however, fortuitous almost always carries the senses both of accident or chance and luck or fortune. It is infrequently used in its sense of “accidental” without the suggestion of good luck, and even less frequently in the sense “lucky” without at least a suggestion of accident or chance
"People object" because it's confusing to use the word 'fortuitous' (which means accidental) if 'fortunate' (which means lucky) is intended, unless the situation happens to also be accidental and the goal is to highlight the chance aspect. I wouldn't "insist" about this, unless working as a copyeditor, but many uses of the word "fortuitous" make it clear that the speaker/writer doesn't really know what the word means, and it often ends up sounding pretentious when people use "fancy" uncommon words incorrectly.
In any case, neither of these words is the right choice in the context of the previous comment. A word like "incredible" or "unlikely" or "amazing" would more clearly express the idea.
> Commissioner Anabell Brumford: Ladies and gentlemen, I would now like to introduce a most special American. Tonight, he is being honoured for his 1000th drug-dealer killed.
> Lt. Frank Drebin: [to applause] Thank you. But, in all honesty, the last three I backed over with my car. Luckily, they turned out to be drug-dealers.
Here, "luckily" gives the dark implication that the police covered up Drebin's killing of three people by posthumously framing them as drug-dealers... and maybe the other 997 people as well. "Luckily" is nicely understated where "amazingly" would be too obvious, and "incredibly" doesn't work at all.
