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In this paper, we first define a Kenmotsu-like statistical manifold (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>K</mi><mo>.</mo><mi>l</mi><mo>.</mo><mi>s</mi><mo>.</mo><mi>m</mi></mrow></semantics></math></inline-formula>) with examples. Then, we switch to Kenmotsu-like statistical submersions (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>K</mi><mo>.</mo><mi>l</mi><mo>.</mo><mi>s</mi><mo>.</mo><mi>s</mi></mrow></semantics></math></inline-formula>), where we investigate the fact that, for such submersions, each fiber is a statistical manifold that is similar to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>K</mi><mo>.</mo><mi>l</mi><mo>.</mo><mi>s</mi><mo>.</mo><mi>m</mi></mrow></semantics></math></inline-formula>, and the base manifold is similar to the Kähler-like statistical manifold. Subsequently, assuming the postulate that the curvature tensor with regard to the affine connections of the total space obeys certain criteria, we analyze such statistical submersions to those developed by Kenmotsu. Lastly, we talk about statistical submersions (SS) with conformal fibers (CFs) that are <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>K</mi><mo>.</mo><mi>l</mi><mo>.</mo><mi>s</mi><mo>.</mo><mi>m</mi></mrow></semantics></math></inline-formula>.