Recount a time when you faced a challenge, setback, or failure.How did it affect you, and what did you learn from the experience?Your essay is an important tool for presenting something you find important that may not come across elsewhere in your application.
In third place was Option #2 on a setback or failure. Always keep in mind why colleges are asking for an essay: they want to get to know you better.
Nearly all selective colleges and universities (as well as many that aren't overly selective) have holistic admissions, and they consider many factors in addition to numerical measures such as grades and standardized test scores.
Introspection and honesty are key with this prompt. The "belief or idea" you explore could be your own, someone else's, or that of a group.
The best essays will be honest as they explore the difficulty of working against the status quo or a firmly held belief.
The essay prompts are designed to encourage reflection and introspection.
If your essay doesn't include some self-analysis, you haven't fully succeeded in responding to the prompt.
Be careful with that opening word "describe"—you'll want to spend much more time analyzing the problem than describing it.
This essay prompt, like all of the options, is asking you to be introspective and share with the admissions folks what it is that you value.
With the ability to write about an "intellectual challenge, a research query, an ethical dilemma," you can essentially write about any issue that you find important.
Note that you do not have to have solved the problem, and some of the best essays will explore problems that need to be solved in the future.