The chance it is just a coincidence, they make one in 15,000, or three sigma. That’s not quite enough for discovery, but it’s a point where you think there may be something in it.

If you had just the one hypothesis ever, and got only a 1 in 15,000 chance that it doesn't exist, that's a near certainty. But if you have thousands of astronomers searching for things then from time to time some of them are bound to hit on a 1 in 15,000 chance just by chance. So you are bound to get a few results of similar probability to this from time to time.

Individually they seem very likely if you are the astronomer who came to this conclusion, when you take into account all the other astronomers looking and the number of hypotheses each one considers in a lifetime - it's not so impressive as it seems at first.

That's why they are not saying "We have proved it", but are being professionally cautious about it, although it may seem at first like a near certainty. You might think they should just say it exists, with, on the face of it, a 99.993% certainty that it exists, but that's not how it works in science.

In particle physics, where the experiments generate huge amounts of data, 3 sigma results are common and are often just clusters, patterns in the noise. Collect enough data and you are bound to see 3 sigma results from time to time even if the data is random. They aim for 5 sigma for discovery.

“Others, like planetary scientist Dave Jewitt, who discovered the Kuiper belt, are more cautious. The 0.007% chance that the clustering of the six objects is coincidental gives the planet claim a statistical significance of 3.8 sigma—beyond the 3-sigma threshold typically required to be taken seriously, but short of the 5 sigma that is sometimes used in fields like particle physics. That worries Jewitt, who has seen plenty of 3-sigma results disappear before. By reducing the dozen objects examined by Sheppard and Trujillo to six for their analysis, Batygin and Brown weakened their claim, he says. “I worry that the finding of a single new object that is not in the group would destroy the whole edifice,” says Jewitt, who is at UC Los Angeles. “It’s a game of sticks with only six sticks.””

from: Astronomers say a Neptune-sized planet lurks beyond Pluto

Still it's intriguing and they claim it's the most likely planet X to date.

The way to be more certain is to spot it in a telescope, and that’s what they are trying to do. They are searching for it with the Subaru telescope in Hawaii. Astronomers Are On A Celestial Treasure Hunt. The Prize? Planet Nine

See also my

Why This New "Planet X" Is No Threat To Earth :).

Would New Planet X Clear Its Orbit? - And Any Better Name Than "Planet Nine"?