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.