Refactor bayesian observations using dataclass (#79590)

* refactor

* remove some changes

* remove typehint

* improve codestyle

* move docstring to comment

* < 88 chars

* avoid short var names

* more readable

* fix rename

* Update homeassistant/components/bayesian/helpers.py

Co-authored-by: epenet <6771947+epenet@users.noreply.github.com>

* Update homeassistant/components/bayesian/binary_sensor.py

Co-authored-by: epenet <6771947+epenet@users.noreply.github.com>

* Update homeassistant/components/bayesian/binary_sensor.py

Co-authored-by: epenet <6771947+epenet@users.noreply.github.com>

* no intermediate

* comment why set before list

Co-authored-by: epenet <6771947+epenet@users.noreply.github.com>

homeassistant/components/bayesian/helpers.py

@@ -0,0 +1,69 @@
+"""Helpers to deal with bayesian observations."""
+from __future__ import annotations
+
+from dataclasses import dataclass, field
+import uuid
+
+from homeassistant.const import (
+    CONF_ABOVE,
+    CONF_BELOW,
+    CONF_ENTITY_ID,
+    CONF_PLATFORM,
+    CONF_VALUE_TEMPLATE,
+)
+from homeassistant.helpers.template import Template
+
+from .const import CONF_P_GIVEN_F, CONF_P_GIVEN_T, CONF_TO_STATE
+
+
+@dataclass
+class Observation:
+    """Representation of a sensor or template observation."""
+
+    entity_id: str | None
+    platform: str
+    prob_given_true: float
+    prob_given_false: float
+    to_state: str | None
+    above: float | None
+    below: float | None
+    value_template: Template | None
+    observed: bool | None = None
+    id: str = field(default_factory=lambda: str(uuid.uuid4()))
+
+    def to_dict(self) -> dict[str, str | float | bool | None]:
+        """Represent Class as a Dict for easier serialization."""
+
+        # Needed because dataclasses asdict() can't serialize Templates and ignores Properties.
+        dic = {
+            CONF_PLATFORM: self.platform,
+            CONF_ENTITY_ID: self.entity_id,
+            CONF_VALUE_TEMPLATE: self.template,
+            CONF_TO_STATE: self.to_state,
+            CONF_ABOVE: self.above,
+            CONF_BELOW: self.below,
+            CONF_P_GIVEN_T: self.prob_given_true,
+            CONF_P_GIVEN_F: self.prob_given_false,
+            "observed": self.observed,
+        }
+
+        for key, value in dic.copy().items():
+            if value is None:
+                del dic[key]
+
+        return dic
+
+    def is_mirror(self, other: Observation) -> bool:
+        """Dectects whether given observation is a mirror of this one."""
+        return (
+            self.platform == other.platform
+            and round(self.prob_given_true + other.prob_given_true, 1) == 1
+            and round(self.prob_given_false + other.prob_given_false, 1) == 1
+        )
+
+    @property
+    def template(self) -> str | None:
+        """Not all observations have templates and we want to get template strings."""
+        if self.value_template is not None:
+            return self.value_template.template
+        return None