According to the counterfactual view, X causes Y if and only if, without X, Y would not exist. Hume interpreted the latter as an ontological view, i.e., as a description of the nature of causality but, given the limitations of the human mind, advised using the former (stating, roughly, that X causes Y if and only if the two events are spatiotemporally conjoined, and X precedes Y) as an epistemic definition of causality. Having an epistemic concept of causality is needed to distinguish between causal and noncausal relations. The contemporary philosophical literature on causality can be divided into five big approaches to causality. These include the (mentioned above) regularity, probabilistic, counterfactual, mechanistic, and manipulationist views. The five approaches can be shown to be reductive, i.e., define causality in terms of relations of other types. According to this reading, they define causality in terms of, respectively, empirical regularities (constant conjunctions of events), changes in conditional probabilities, counterfactual conditions, mechanisms underlying causal relations, and invariance under intervention. Geometrical significance
Causality has the properties of antecedence and contiguity. These are topological, and are ingredients for space-time geometry. As developed by Alfred Robb, these properties allow the derivation of the notions of time and space. Max Jammer writes "the Einstein postulate ... opens the way to a straightforward construction of the causal topology ... of Minkowski space." Causal efficacy propagates no faster than light.Thus, the notion of causality is metaphysically prior to the notions of time and space.
So, the short circuit is an INUS condition for the occurrence of the house burning down. Contrasted with conditionals
Conditional statements are not statements of causality. An important distinction is that statements of causality require the antecedent to precede or coincide with the consequent in time, whereas conditional statements do not require this temporal order. Confusion commonly arises since many different statements in English may be presented using "If ..., then ..." form (and, arguably, because this form is far more commonly used to make a statement of causality). The two types of statements are distinct, however. For example, all of the following statements are true when interpreting "If ..., then ..." as the material conditional:

If Barack Obama is president of the United States in 2011, then Germany is in Europe. If George Washington is president of the United States in 2011, then ⟨arbitrary statement⟩.The first is true since both the antecedent and the consequent are true. The second is true in sentential logic and indeterminate in natural language, regardless of the consequent statement that follows, because the antecedent is false. The ordinary indicative conditional has somewhat more structure than the material conditional. For instance, although the first is the closest, neither of the preceding two statements seems true as an ordinary indicative reading. But the sentence:

If Shakespeare of Stratford-on-Avon did not write Macbeth, then someone else did.intuitively seems to be true, even though there is no straightforward causal relation in this hypothetical situation between Shakespeares not writing Macbeth and someone elses actually writing it.