Solar-wind forecasting is critical for predicting events which can affect Earth's technological systems.  Typically, forecasts combine coronal model outputs with solar-wind models to predict near-Earth conditions. Ensemble forecasting generates sets of outputs to create probabilistic forecasts which quantify forecast uncertainty, vital for reliable/actionable forecasts. We adapt meteorological methods to create a calibrated solar-wind ensemble and probabilistic forecast for ambient solar wind, a prerequisite for accurate coronal mass ejection (CME) forecasting. Calibration is achieved by adjusting ensemble inputs/outputs to align the ensemble spread with observed event frequencies. We produce hindcasts in near-Earth space using coronal-model output over Solar Cycle 24, as input to Heliospheric Upwind eXtrapolation with time dependence (HUXt) solar-wind model. Making spatial perturbations to the coronal model output at 0.1AU, we produce ensembles of inner-boundary conditions for HUXt, evaluating how forecast accuracy was impacted by the scales of perturbations applied. We found optimal spatial perturbations described by Gaussian distributions with variances of 20 degrees latitude and 10 degrees longitude; these might represent spatial uncertainty within the coronal model. This produced probabilistic forecasts better matching observed frequencies.  Calibration improved forecast reliability, reducing the Brier score by 9% and forecast decisiveness increasing AUC ROC score by 2.5%. Improvements were subtle but systematic. Additionally, we explored statistical post-processing to correct over-confidence bias, improving forecast actionability. However, this method, applied post-run, does not affect the solar-wind state used to propagate CMEs. This work represents the first formal calibration of solar-wind ensembles, laying groundwork for comprehensive forecasting systems like a calibrated multi-model ensemble.