Many recent data-driven studies have used sensor profile data for prognostics and health management (PHM). However, existing data-driven PHM techniques are vulnerable to three types of uncertainty: sensor noise inherent to the sensor profile data, uncertainty regarding the current health status diagnosis caused by monitoring a single health index (HI), and uncertainty in predicting the remaining useful life (RUL), which is affected by unpredictable changes in system operating conditions and the future external environment. This study proposes a deep conditional health index extraction network (DCHIEN) for PHM to effectively manage these three types of uncertainty. DCHIEN is a model that combines a stacked denoising autoencoder that extracts high-level features robust to sensor noise with a feed-forward neural network that produces an HI based on user-defined monitoring conditions. This approach supports system health monitoring using the conditional HI, as well as prognostics using RUL interval predictions. Extensive experiments were conducted using NASA's turbofan engine degradation dataset. The results show that the proposed method achieves a superior RUL prediction performance compared to state-of-the-art methods and that uncertainties can be effectively managed.