Probabilistic forecasting of irregularly sampled multivariate time series with missing values is an important problem in many fields, including health care, astronomy, and climate. State-of-the-art methods for the task estimate only marginal distributions of observations in single channels and at single timepoints, assuming a fixed-shape parametric distribution. In this work, we propose a novel model, ProFITi, for probabilistic forecasting of irregularly sampled time series with missing values using conditional normalizing flows. The model learns joint distributions over the future values of the time series conditioned on past observations and queried channels and times, without assuming any fixed shape of the underlying distribution. As model components, we introduce a novel invertible triangular attention layer and an invertible non-linear activation function on and onto the whole real line. We conduct extensive experiments on four datasets and demonstrate that the proposed model provides $4$ times higher likelihood over the previously best model.