There's a lot of sibling comments going on about whether the value they're looking at is the right one. What the Times is showing as their headline number is Positive Predictive Value (True positive/(TP+FP)), which depends on the prevalence in the population. The "methods section" here is a little vague, but given the low prevalence I'm willing to accept on face value that it's basically accurate (i.e. that it's not assuming that the families getting these tests are not orders of magnitude more likely to be positive for these diseases). If the test result truly said one patient's 'daughter had a “greater than 99/100” probability of being born with Patau syndrome', then that's concerning, but given the fairly narrow quotes around the number, I'd suspect that what is actually on the test result is not inconsistent with the fairly low PPV on these screens.
