Probabilistic reasoning stands as a potent method of handling uncertainty in the realm of Artificial Intelligence (AI). At its core, it provides a robust framework for formulating and solving problems that exist in an environment characterized by uncertainty. This method employs the principles of probability theory to make anticipatory predictions, draw inferences, and update knowledge based on new data.

Probabilistic reasoning in AI incorporates various distinguishable features:

• Modeling Uncertainty: This method sufficiently models the uncertainty inherent in practical situations, such as incomplete or ambiguous data.
• Inference: Given a set of data, probabilistic reasoning utilizes inference rules to draw critical conclusions or make predictions.
• Learning: This implies the capability to learn from data—a powerful feature that makes probabilistic models highly adaptable and able to update their predictions based on new information.
• Operational Flexibility: Probabilistic reasoning reflects an ability to operate comfortably with complex, real-world situations.
• Robustness: Owing to its roots in mathematically rigorous probability theory, this approach exhibits a high level of tolerance to erratic data.

Effective implementation of probabilistic reasoning in AI necessitates a thoughtful and sound strategy. It must suitably involve:

• Defining the Problem: Identify and clearly define the problem to be solved.
• Data Collection: Assemble high-quality, relevant data as the backbone of the probabilistic reasoning model.
• Model Selection: Depending upon the problem, select the appropriate probabilistic model such as Bayesian Networks, Markov Models, etc.
• Training the Model: Input the collected data into the selected model and train it.
• Testing and Refinement: Test the predictions and outcomes, refine the model accordingly and reassess it.
• Robust Implementation: Factor in supporting the model to make decisions in real-time in production environments.

Embracing a well-planned strategy will aid in the successful implementation of probabilistic reasoning in AI. It contributes to intelligent decision-making, accelerating the advancement of AI, thus driving wider adoption in diverse industries. However, an exploration of its potential should harbour an equal emphasis on understanding its setbacks – something vital to illuminate its core benefits and ward off potential pitfalls.

The implementation of probabilistic reasoning in AI posits several advantages:

• Robust Decision Making: Probabilistic reasoning allows machines to make informed decisions, despite the prevalence of uncertainty, thereby enhancing their decision-making process.
• Tailored Predictions: By analyzing the available data and trends, it provides targeted and more precise predictions, a feature vital in sectors such as medical diagnostics, financial forecasting, and more.
• Learning Capability: The ability to learn and update knowledge based on recent experiences or data, enables AI systems to grow smarter over time.
• Flexibility: Due to the inherent adaptability of probabilistic reasoning, it can seamlessly handle complex real-world situations, thereby demonstrating operational flexibility.
• Risk Assessment: By providing a measure of certainty to predictions, probabilistic reasoning fortifies AI's capability in effective risk management.

Despite these advantages, this reasoning method is not without its share of challenges.

Bringing into focus the limitations inherent in probabilistic reasoning in AI, they include:

• Complex Calculations: This reasoning method often requires complex, computationally expensive calculations, particularly as the amount of data or the number of variables surges.
• Dependence on Quality of Data: It heavily relies on data for predictions and inferences. Poor quality or inadequate data could result in less accurate or skewed results.
• Probability Interpretation: Finding the right probability interpretation—frequentist or Bayesian—can be dispute-ridden.
• Data Privacy Concerns: The requirement for large volumes of data could infringe upon privacy norms, elevating legal and ethical concerns.
• Integration Issues: The integration of probabilistic reasoning algorithms with existing systems or technologies can prove challenging.