The answer: Slim, if history repeats itself.
A look at asylum denial rates show extreme variances between the nationalities of people applying.
And Guatemala, Honduras and El Salvador -- the three countries represented in this caravan
-- have among the highest US asylum denial rates, according to Syracuse University's Transactional Records Access Clearinghouse
But asylum seekers from Mexico and Haiti fared even worse.
On the flip side, some nationalities rarely have their asylum attempts turned down.
Why is this?
There's no simple answer, but there are definitely key factors.
"Country conditions always can have a big influence over whether you have legitimate grounds for asylum or not," TRAC co-director Susan B. Long said.
Another hugely important aspect is whether the asylum seeker has an attorney.
"Without representation, the deck is stacked against an asylum seeker," TRAC said.
In fact, "your odds are five times better to get asylum if you have an attorney," Long said.
Take, for example, China. Between October 2011 and September 2017, China had the highest number of total US asylum decisions (31,176) -- and one of the lowest denial rates (20.3%).
It's no surprise that more than 95% of those Chinese applicants had attorneys.
Other nationalities with low denial rates include Egypt, Ethiopia, Syria and Burkina Faso. All had attorney representation in more than 89% percent of cases decided in that time frame.
But those who show up for crucial interviews
with neither an attorney nor English skills often get denied more.
"A lot don't have the resources to pay for it," Long said. "There are a lot of attorneys trying to be of pro bono assistance, but the need is great."
Of course, there are many factors US officials weigh when deciding
whether to grant someone asylum, such as whether they have proof of persecution or a well-founded fear of persecution
due to race, religion, national origin, political opinion or membership in a particular social group.
But "(t)here are no mandatory bars to establishing a credible fear or persecution or torture," US Citizenship and Immigration Services