You keep using that word. I don’t think it means what you think it means.
— Inigo Montoya, The Princess Bride
The Princess Bride introduces us to a trio of kidnapers, hired by Humperdinck to kidnap and murder Buttercup. The leader is Vizzini, a self proclaimed Sicilian man of genius and the brains of the operation. He is smug, ruthless, and is overly fond of the word inconceivable. He loses a battle of wits against Westly and dies of poison.
I cannot believe I lost! This is absolutely inconceivable! INCONCEIVABLE! *falls over dead*
— Vizzini, The Princess Bride
So what does it mean?
Something inconceivable is impossible even to imagine, nothingness, infinity or the sound of one hand clapping, that sort of thing. In a strictly biological sense it can mean impossible to conceive, such as an inter-species crossbreed, goat molestation resulting in the birth of a satyr would be inconceivable.
Since anything that is truly and utterly inconceivable would by definition be unimaginable in any way, even the concept couldn’t be conceived of in our minds, as we’re not designed to process such impossible concepts. This means that the word practically invites us to use it for hyperbole.
In any case, it does not mean “impossible”, “highly unlikely”, or “unfortunate”. For example, while juggling knives you drop them all and they land forming a perfect circle. It would be unlikely for them all to land point down in the floor. While it would be unfortunate, if they landed point first in your foot. If they defied gravity and shot off into outer space, that would be impossible. The circle having a π of 3, now that would be inconceivable.
Language evolves. Over time some words may take on new meanings, or old meanings may fall into disuse. This is a process that language scholars call semantic drift and given enough time alters the word to the point that the modern meaning is radically different from the original usage.
Awful used to mean “full of awe and worthy of respect” and in Shakespeare’s day you could have congratulated someone on their awful work. Today you’d probably use awesome.
It’s happening all the time, you can’t ignore it and stick with the old meaning. When was the last time you heard someone (who wasn’t trying to be funny — and likely failing) use “gay” to mean anything other than “homosexual” or as a disparaging term?