Thesarus.com is your friend. "Miracle" synonyms:

marvel
phenomenon
rarity
revelation
surprise
wonder

I feel comfortable with mystery in life.

I have also wished there was a better term than miracle that doesn’t have religious connotations. I still find myself using it—rarely, but when I do, I usually catch myself, and change it to something like “fucking remarkable” for extra emphasis.

What about miracle whip lol

How about these alternatives to miracle or miraculous:
amazing event;
astonishing,
astounding,
awesome,
incredible,
fabulous,
mind-bending,
mind-blowing
mind-boggling,
phenomenal,
portentous,
prodigious,
stunning,
stupendous,
unbelievable,
unimaginable,
wondrous

It's a wonder.
It's a marvel, a happy mystery.

Anything more equivalent than that would imply magic, which is what I assume you wish to avoid.

I have always used the term 'beautiful surprise' to denote things a more religious person would deem a miracle by divine intervention. I like serendipity, too, and it's also quite fitting as others have noted. Though I see serendipity as more fitting to describe a result than a forethought.

Yes I do not think that there is a neat single word. I always have to resort to phrases like. "Wonderful good fortune." Which is not very satisfactory. I think that AmytheBruce below comes up with the closest, 'serendipity' though that is not perfect since its has slightly trivial associations. Why not invent one yourself, and persuade this site to begin promoting it ?

How about something like an, "incredibility".

It's probably because of two things:

1. Lack of knowledge on probabilities. The fact that something is extremely unlikely to happen, does not equal to impossible.

2. Because the moment something improbable happens to people, they link it to god; surprise surpise, the god of their country. Thus, Christ did it, is the most possible outcome, thus they call it a miracle.

You say miracle and I think mayonnaise. That's what a lifetime of atheism will do to you.

I’m just fine with phenomenon or wonder. I even use miracle and am ok with that too, because it just means something wonderful which has no evident attributable cause, much like many other unanswered questions about the how and why of our existence and place in the universe. No need to imbue it with supernatural meaning, it just means we are at present unable to understand how or why it happened, but that there’s a logical explanation just the same.

How about "magic"?

Because miracle's don't happen, just extraordinary circumstances, none of which ever violate the laws of nature.
Perhaps the word you're looking for is "synchronicity."

syn·chro·nic·i·ty
/ˌsiNGkrəˈnisədē/

noun

1. the simultaneous occurrence of events which appear significantly related but have no discernible causal connection.

Take a familiar use of the word and apply the alternatives and see which, if any, work best. For this exercise we;ll use the movie Miracle on 34th Street.

Incredibility on 34th Street
Serendipity on 34th Street
Amazement on 34th Street
Thaumaturgy on 34th Street
Sensation on 34th Street
Big Surprise on 34th Street
Unlikely Phenomenon on 34th Street
Rare Supernatural Occurence on 34th Street

Do any of those work for anyone? I might be able to live with "Sensation" but I'd rather just keep Miracle and live with the religious implications.

The movie The Miracle Worker would be another good exercise.

I agree about the word "miracle", but I don't think that "luck" is much better as even it implies some sort of causative force behind events.

How about "serendipity"? Meaning "the occurrence and development of events by chance in a happy or beneficial way."

Definition of Miracle......An event that appears inexplicable by the laws of nature and so is held to be supernatural in origin or an act of God.
As Atheists and Agnostics we know that there are no supernatural events and there is no God so we we should not use the word miracle to describe any event.

I say we take back the word.

I am a common person and most of the common people I know think that the word "miracle" has something to do with a god. (of course, it just happens to be their god.) Whatever word is used here it means "something they cannot explain" and so any of us take that into "supernatural" which really means the same thing. It is something you cannot explain. BTW, I no longer believe in the supernatural but I know there is so much that we cannot explain.

Try "unexplained event".

Stupendous

That is fricking stupendous!
It's a stupendous event!

With billions of people on the planet, something "that happens to only one in a hundred" is a pretty common event.

The word is FICTION = miracle ....religion = FICTION .... WHY would a self respecting Atheist pretend a miracle may happen in the future when zero miracles have ever happened since the 1st shamanS invented religionS ???

I like "fortune" with different qualifiers..."some" "good", "great" "fantastic" "un-believeable", ect. I use to like "luck", but then I said "good luck" and was accused of sarcasm.

I find myself using the word miracle as " damn near impossible".
I say "It would take a miracle..." as someone else would say "you have a better chance winning the lottery".
I do like the song Miracles by Jefferson Starship though.

As Aron Ra says look up the defunitions of miracle and magic. They are almost indistinguishable.

Sorry, I cheated I looked in a thesaurus there are a shitload of synonyms. But as others have said, lucky, serendipity, which I kind of like the 3rd Doctor used serendipity.