I suck at probability. Help me solve an easy problem?

Nope you have 99.40% chance of winning (10,000/10060)

Fortunately no :-P You have a 10,000 in 10,060 chance to win, so about 99.4% ;-)

That's currently 10.000 / 10.060, slightly below 100%

it means 60 people are gonna get the shaft. If I had entered, I'm sure I'd be one of those 60

Your chance of winning is (100/10060)*10000 = 99.4%

The probability of winning is p = 10,000 / 10,060 ≈ 0.994. Hence, the chance is c = p / (1 − p) ≈ 166.6667 to 1.

You have a 1 in 167 chance NOT to win a copy.

Pobability is generally the result you're looking for divided by all the results.
You want to roll a dice and get a 6. The dice have 6 sides, but only one is good for you: so probability of that is 1 divided by 6, 1/6.
If 1 and 2 are the numbers you want to get, that means that 2 results are good for you out of the 6, so the probability is 2 / 6

With the giveaway, there is 10k copies, and any of them is good for you, as you just want to win one. The chance of YOU winning out of the 10.060 people is 1 (as YOU, as one person, want to win) out of 10.060. But as there is 10k copies, basically you multiply this by 10.000, as each of the copies get to a random person, and you have 1/10060 chance for winning each piece:
For giveaways in short: it's (copies) / (entries)

The number of entries will grow, but in the end you will have at least, 66% of chances of winning, I suppose.

Wow, thanks for the quick and educational responses, fellas. I knew 1 in 60 couldn't be right, but I couldn't figure out why.

It's 50%.
Either you win or you die.

You, no.
Me, yes.

I once pissed on hospitality and it haunts me ever since.

Won't bump, Puzzle is way too hard
since you already got a lot of great answers, I thought I'd do the honors and be the first to shitpost. (Although I was obviously way too slow) Please don't eat me Mr. Dinosaur :'(

I hope you are joking

Since I haven't got an answer elsewhere, another dumb question: What's a guib? I've heard others mention it, but not in a context I completely understand (except for when it is said that there are no guibs in the post...)

don't try to troll me, dino

you roll a dice with 10600 faces 10000 times hoping to get face x once
http://www.madandmoonly.com/doctormatt/mathematics/dice1.pdf

There is a non-mathematical aspect too: after the GA is over, one can still try winning dozens/hundreds of re-gifted copies :-)