A word for absolutely predictive
In biology, most things are predictive: Toxicity is given in LD50, but one cannot know which half of the population will die, 1% of kids will be born with some type of autism, but we don't know which kids (obviously, there are risk factors, but nothing is absolute), etc....
On the other hand, if I combine water with an acid, it absolutely heats up. If I drop my coffee cup, it's absolutely falling to the floor. (A pedant might mention that the coffee cup doesn't fall in space, but that gets to the heart of the matter - there are preconditions that we understand in physics, but as sciences get softer, those preconditions become less well understood - I assume that as Biology matures, we will understand better those).
I need two words which emphasize the difference between A often causes or predicts B and A must cause B.
Solution 1:
There are some good suggestions in the comments, which I'm going to pick from in my answer. All definitions from Merriam-Webster unless otherwise noted.
A guarantees B
Guarantee: an assurance for the fulfillment of a condition
A invariably causes B
Invariably: on every occasion
A makes B certain / A makes B certain to occur
Certain: (3a) dependable, reliable - (a certain remedy for the disease)
(3b) known or proved to be true : indisputable (it is certain that we exist)
(4a) inevitable (the certain advance of age)
(4b) incapable of failing : destined - used with a following infinitive (she is certain to do well)
A necessitates B
Necessitate: to make necessary, to force or compel
A is sufficient for B / A is a sufficient condition for B
Sufficient Condition: a state of affairs whose existence assures the existence of another state of affairs. Note: This is common wording amongst philosophers, mathematicians and logicians, but it could sound odd in other contexts.
B is necessary for A / B is a necessary condition for A
Necessary Condition: a proposition whose falsity assures the falsity of another. Note: This is common wording amongst philosophers, mathematicians and logicians, but it could sound odd in other contexts.
I can't think of many options for cases when the causal relationship is specifically probabilistic. Again, philosophers have a word for it:
A probabilifies B
Probabilify: to make probable, give probability to (Oxford Living Dictionaries)