Probability is not my strong suit but this is what i think.
P= number of ways 4 can be chosen from 14 / number of ways 4 can be chosen from 17
P= 14C4 / 17C4
P = 1001 / 2380
$$\mbox{P(all 3 survive) }=\frac{1001}{2380}=\frac{143}{340}$$
$${\frac{{\mathtt{1\,001}}}{{\mathtt{2\,380}}}} = {\frac{{\mathtt{143}}}{{\mathtt{340}}}} = {\mathtt{0.420\: \!588\: \!235\: \!294\: \!117\: \!6}}$$
Can another mathematician please check this - I'm fairly confident that it is correct.