This paper studies the estimation of the conditional density f(x,⋅) of Yi given Xi=x, from the observation of an i.i.d. sample (Xi,Yi)∈ℝ^d, i∈{1,…,n}. We assume that f depends only on r unknown components with typically r≪d.We provide an adaptive fully-nonparametric strategy based on kernel rules to estimate f. To select the bandwidth of our kernel rule, we propose a new fast iterative algorithm inspired by the Rodeo algorithm (Wasserman and Lafferty, 2006) to detect the sparsity structure of f. More precisely, in the minimax setting, our pointwise estimator, which is adaptive to both the regularity and the sparsity, achieves the quasi-optimal rate of convergence. Our results also hold for (unconditional) density estimation. The computational complexity of our method is only O(dnlogn). A deep numerical study shows nice performances of our approach.