In some respects, that's not always the case. Some competitions have multiple winners, or at least multiple parties who "make the cut." The best example I can think of in my other industry of music is getting a gig at a particular venue. Whether it is a club, concert hall, restaurant, or wherever, there are probably a limited number of available slots for an artist to perform, so the goal is to fill those slots with a variety of acts so as not to saturate the event. One musician is not necessarily going to play every Saturday night at the same restaurant; there is probably a rotation of musicians who come in over a set period of time. Therefore, if the competition is between getting the gig and not getting the gig in this case, you have a better chance of succeeding, and your success does not automatically equal the failure of someone else.
However, it is very easy to forget this. No matter the industry, our failure can easily seep into our thoughts when we see someone else succeed, especially when it has no correlation to our situation! If I see a colleague succeeding at a gig at a restaurant where I once tried to get a gig years prior, why am I jealous? That doesn't mean that I am not a successful musician! I can have tons of other gigs that allow me to perform and compensate me, but the fact that I didn't get that one gig and someone else did still irks me. These are the situations where many of us need to take the additional time to think through these thoughts and readjust our views.
If a baseball roster has 25 guys on it, then 25 guys are going to make the cut, not just one. Sure, there may be competition to earn a specific spot, but pulling the lens back will show that the example is somewhat similar to the idea above.
The point is that competition sometimes leads us to become jealous or wish even wish failure on others when it really has to bearing to our success. Our paths sometimes lead us to something greater, and we have to be open and awake to that.