Few circumstances are completely uncertain; there's usually some underlying certainty involved. Probabilistic thinking recognizes and exploits the underlying certainty. Normal life uses probabilistic thinking for prediction; scientific life also uses it in other ways, such as for modeling, as in errors in measurements, or fundamental explanations, as in quantum mechanics a la Copenhagen.
Several probabilistic thinking styles exist, and several are needed. For example, classical probabilistic thinking excludes independence, an important idea for quantum probabilistic thinking. In addition, other areas - such as mathematics and computation - have thinking styles related to, but different from, probabilistic thinking.
Probabilistic thinking can be subjective (belief based) or scientific (objective). Scientific objectivity recognizes and accommodates the judgments underlying probabilistic thinking; subjective thinking leaves these judgments unrecognized. Studying probability as an end is largely unhelpful; probabilistic thinking must be grounded in the uncertainty of the world to be helpful. Probabilistic thinking is difficult, but less formal styles are easier to learn and use.
But before we can quantify uncertainty, we need some tools.