In recommendation scenarios, there are two long-standing challenges, i.e., selection bias and data sparsity, which lead to a significant drop in prediction accuracy for both Click-Through Rate (CTR) and post-click Conversion Rate (CVR) tasks. To cope with these issues, existing works emphasize on leveraging Multi-Task Learning (MTL) frameworks (Category 1) or causal debiasing frameworks (Category 2) to incorporate more auxiliary data in the entire exposure/inference space D or debias the selection bias in the click/training space O. However, these two kinds of solutions cannot effectively address the not-missing-at-random problem and debias the selection bias in O to fit the inference in D. To fill the research gaps, we propose a Direct entire-space Causal Multi-Task framework, namely DCMT, for post-click conversion prediction in this paper. Specifically, inspired by users' decision process of conversion, we propose a new counterfactual mechanism to debias the selection bias in D, which can predict the factual CVR and the counterfactual CVR under the soft constraint of a counterfactual prior knowledge. Extensive experiments demonstrate that our DCMT can improve the state-of-the-art methods by an average of 1.07% in terms of CVR AUC on the five offline datasets and 0.75% in terms of PV-CVR on the online A/B test (the Alipay Search). Such improvements can increase millions of conversions per week in real industrial applications, e.g., the Alipay Search.