No because conditioning is fundamentally a 'selection' operation. It selects/filters the full data on, say, a predicate (say gender==male) and analyses that subset. This is fundamentally different from an intervention where you turn someone into 'male' who wasn't male to begin with. Those who were turned male might behave differently from those who were male without any intervention -- the sub-population you selected for defining conditional probabilities.

These two scenarios have the potential to exhibit different behavior -- probabilistic models without a notion of intervention or counterfactuals will only capture the former. But just like this 'selection' operator you c an define an analogous operator for -- selecting on those that you interved on -- then you are in the realms of causality.